The study of chance processes or the relative frequency characterizing a chance process.
The branch of mathematics dealing with the purely logical properties of probability. Its theorems underlie most statistical methods. (Last, A Dictionary of Epidemiology, 2d ed)
Usually refers to the use of mathematical models in the prediction of learning to perform tasks based on the theory of probability applied to responses; it may also refer to the frequency of occurrence of the responses observed in the particular study.
Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.
A theorem in probability theory named for Thomas Bayes (1702-1761). In epidemiology, it is used to obtain the probability of disease in a group of people with some characteristic on the basis of the overall rate of that disease and of the likelihood of that characteristic in healthy and diseased individuals. The most familiar application is in clinical decision analysis where it is used for estimating the probability of a particular diagnosis given the appearance of some symptoms or test result.
A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.
Computer-based representation of physical systems and phenomena such as chemical processes.
A stochastic process such that the conditional probability distribution for a state at any future instant, given the present state, is unaffected by any additional knowledge of the past history of the system.
Theoretical representations that simulate the behavior or activity of genetic processes or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.
Elements of limited time intervals, contributing to particular results or situations.
In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993)
Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.
Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.
Processes that incorporate some element of randomness, used particularly to refer to a time series of random variables.
Functions constructed from a statistical model and a set of observed data which give the probability of that data for various values of the unknown model parameters. Those parameter values that maximize the probability are the maximum likelihood estimates of the parameters.
Application of statistical procedures to analyze specific observed or assumed facts from a particular study.
Establishing the father relationship of a man and a child.
The opening and closing of ion channels due to a stimulus. The stimulus can be a change in membrane potential (voltage-gated), drugs or chemical transmitters (ligand-gated), or a mechanical deformation. Gating is thought to involve conformational changes of the ion channel which alters selective permeability.
In screening and diagnostic tests, the probability that a person with a positive test is a true positive (i.e., has the disease), is referred to as the predictive value of a positive test; whereas, the predictive value of a negative test is the probability that the person with a negative test does not have the disease. Predictive value is related to the sensitivity and specificity of the test.
A theoretical technique utilizing a group of related constructs to describe or prescribe how individuals or groups of people choose a course of action when faced with several alternatives and a variable amount of knowledge about the determinants of the outcomes of those alternatives.
Binary classification measures to assess test results. Sensitivity or recall rate is the proportion of true positives. Specificity is the probability of correctly determining the absence of a condition. (From Last, Dictionary of Epidemiology, 2d ed)
An aspect of personal behavior or lifestyle, environmental exposure, or inborn or inherited characteristic, which, on the basis of epidemiologic evidence, is known to be associated with a health-related condition considered important to prevent.
The statistical reproducibility of measurements (often in a clinical context), including the testing of instrumentation or techniques to obtain reproducible results. The concept includes reproducibility of physiological measurements, which may be used to develop rules to assess probability or prognosis, or response to a stimulus; reproducibility of occurrence of a condition; and reproducibility of experimental results.
Mathematical or statistical procedures used as aids in making a decision. They are frequently used in medical decision-making.
Evaluation undertaken to assess the results or consequences of management and procedures used in combating disease in order to determine the efficacy, effectiveness, safety, and practicability of these interventions in individual cases or series.
An electrophysiologic technique for studying cells, cell membranes, and occasionally isolated organelles. All patch-clamp methods rely on a very high-resistance seal between a micropipette and a membrane; the seal is usually attained by gentle suction. The four most common variants include on-cell patch, inside-out patch, outside-out patch, and whole-cell clamp. Patch-clamp methods are commonly used to voltage clamp, that is control the voltage across the membrane and measure current flow, but current-clamp methods, in which the current is controlled and the voltage is measured, are also used.
Statistical models which describe the relationship between a qualitative dependent variable (that is, one which can take only certain discrete values, such as the presence or absence of a disease) and an independent variable. A common application is in epidemiology for estimating an individual's risk (probability of a disease) as a function of a given risk factor.
Studies used to test etiologic hypotheses in which inferences about an exposure to putative causal factors are derived from data relating to characteristics of persons under study or to events or experiences in their past. The essential feature is that some of the persons under study have the disease or outcome of interest and their characteristics are compared with those of unaffected persons.
Graphical representation of a statistical model containing scales for calculating the prognostic weight of a value for each individual variable. Nomograms are instruments that can be used to predict outcomes using specific clinical parameters. They use ALGORITHMS that incorporate several variables to calculate the predicted probability that a patient will achieve a particular clinical endpoint.
Observation of a population for a sufficient number of persons over a sufficient number of years to generate incidence or mortality rates subsequent to the selection of the study group.
The voltage differences across a membrane. For cellular membranes they are computed by subtracting the voltage measured outside the membrane from the voltage measured inside the membrane. They result from differences of inside versus outside concentration of potassium, sodium, chloride, and other ions across cells' or ORGANELLES membranes. For excitable cells, the resting membrane potentials range between -30 and -100 millivolts. Physical, chemical, or electrical stimuli can make a membrane potential more negative (hyperpolarization), or less negative (depolarization).
The complete summaries of the frequencies of the values or categories of a measurement made on a group of items, a population, or other collection of data. The distribution tells either how many or what proportion of the group was found to have each value (or each range of values) out of all the possible values that the quantitative measure can have.
A class of statistical procedures for estimating the survival function (function of time, starting with a population 100% well at a given time and providing the percentage of the population still well at later times). The survival analysis is then used for making inferences about the effects of treatments, prognostic factors, exposures, and other covariates on the function.
A prediction of the probable outcome of a disease based on a individual's condition and the usual course of the disease as seen in similar situations.
The qualitative or quantitative estimation of the likelihood of adverse effects that may result from exposure to specified health hazards or from the absence of beneficial influences. (Last, Dictionary of Epidemiology, 1988)
A method of comparing the cost of a program with its expected benefits in dollars (or other currency). The benefit-to-cost ratio is a measure of total return expected per unit of money spent. This analysis generally excludes consideration of factors that are not measured ultimately in economic terms. Cost effectiveness compares alternative ways to achieve a specific set of results.
Age as a constituent element or influence contributing to the production of a result. It may be applicable to the cause or the effect of a circumstance. It is used with human or animal concepts but should be differentiated from AGING, a physiological process, and TIME FACTORS which refers only to the passage of time.
The act of making a selection among two or more alternatives, usually after a period of deliberation.
A graphic means for assessing the ability of a screening test to discriminate between healthy and diseased persons; may also be used in other studies, e.g., distinguishing stimuli responses as to a faint stimuli or nonstimuli.
Studies in which individuals or populations are followed to assess the outcome of exposures, procedures, or effects of a characteristic, e.g., occurrence of disease.
The condition in which reasonable knowledge regarding risks, benefits, or the future is not available.
The study of the generation and behavior of electrical charges in living organisms particularly the nervous system and the effects of electricity on living organisms.
Studies in which subsets of a defined population are identified. These groups may or may not be exposed to factors hypothesized to influence the probability of the occurrence of a particular disease or other outcome. Cohorts are defined populations which, as a whole, are followed in an attempt to determine distinguishing subgroup characteristics.
Sequential operating programs and data which instruct the functioning of a digital computer.
The communication from a NEURON to a target (neuron, muscle, or secretory cell) across a SYNAPSE. In chemical synaptic transmission, the presynaptic neuron releases a NEUROTRANSMITTER that diffuses across the synaptic cleft and binds to specific synaptic receptors, activating them. The activated receptors modulate specific ion channels and/or second-messenger systems in the postsynaptic cell. In electrical synaptic transmission, electrical signals are communicated as an ionic current flow across ELECTRICAL SYNAPSES.
A measurement index derived from a modification of standard life-table procedures and designed to take account of the quality as well as the duration of survival. This index can be used in assessing the outcome of health care procedures or services. (BIOETHICS Thesaurus, 1994)
A graphic device used in decision analysis, series of decision options are represented as branches (hierarchical).
Specialized junctions at which a neuron communicates with a target cell. At classical synapses, a neuron's presynaptic terminal releases a chemical transmitter stored in synaptic vesicles which diffuses across a narrow synaptic cleft and activates receptors on the postsynaptic membrane of the target cell. The target may be a dendrite, cell body, or axon of another neuron, or a specialized region of a muscle or secretory cell. Neurons may also communicate via direct electrical coupling with ELECTRICAL SYNAPSES. Several other non-synaptic chemical or electric signal transmitting processes occur via extracellular mediated interactions.
Procedures for finding the mathematical function which best describes the relationship between a dependent variable and one or more independent variables. In linear regression (see LINEAR MODELS) the relationship is constrained to be a straight line and LEAST-SQUARES ANALYSIS is used to determine the best fit. In logistic regression (see LOGISTIC MODELS) the dependent variable is qualitative rather than continuously variable and LIKELIHOOD FUNCTIONS are used to find the best relationship. In multiple regression, the dependent variable is considered to depend on more than a single independent variable.
Theoretical representations that simulate the behavior or activity of the neurological system, processes or phenomena; includes the use of mathematical equations, computers, and other electronic equipment.
The process of making a selective intellectual judgment when presented with several complex alternatives consisting of several variables, and usually defining a course of action or an idea.
Use of electric potential or currents to elicit biological responses.
A set of techniques used when variation in several variables has to be studied simultaneously. In statistics, multivariate analysis is interpreted as any analytic method that allows simultaneous study of two or more dependent variables.
Any detectable and heritable change in the genetic material that causes a change in the GENOTYPE and which is transmitted to daughter cells and to succeeding generations.
The return of a sign, symptom, or disease after a remission.
The rate dynamics in chemical or physical systems.
A field of biology concerned with the development of techniques for the collection and manipulation of biological data, and the use of such data to make biological discoveries or predictions. This field encompasses all computational methods and theories for solving biological problems including manipulation of models and datasets.
The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)
Depolarization of membrane potentials at the SYNAPTIC MEMBRANES of target neurons during neurotransmission. Excitatory postsynaptic potentials can singly or in summation reach the trigger threshold for ACTION POTENTIALS.
A basic element found in nearly all organized tissues. It is a member of the alkaline earth family of metals with the atomic symbol Ca, atomic number 20, and atomic weight 40. Calcium is the most abundant mineral in the body and combines with phosphorus to form calcium phosphate in the bones and teeth. It is essential for the normal functioning of nerves and muscles and plays a role in blood coagulation (as factor IV) and in many enzymatic processes.
Family in the order COLUMBIFORMES, comprised of pigeons or doves. They are BIRDS with short legs, stout bodies, small heads, and slender bills. Some sources call the smaller species doves and the larger pigeons, but the names are interchangeable.
Abrupt changes in the membrane potential that sweep along the CELL MEMBRANE of excitable cells in response to excitation stimuli.
The pattern of any process, or the interrelationship of phenomena, which affects growth or change within a population.
The total number of cases of a given disease in a specified population at a designated time. It is differentiated from INCIDENCE, which refers to the number of new cases in the population at a given time.
Cell membrane glycoproteins that are selectively permeable to potassium ions. At least eight major groups of K channels exist and they are made up of dozens of different subunits.
The science and art of collecting, summarizing, and analyzing data that are subject to random variation. The term is also applied to the data themselves and to the summarization of the data.
The time from the onset of a stimulus until a response is observed.
The proportion of survivors in a group, e.g., of patients, studied and followed over a period, or the proportion of persons in a specified group alive at the beginning of a time interval who survive to the end of the interval. It is often studied using life table methods.
Continuous frequency distribution of infinite range. Its properties are as follows: 1, continuous, symmetrical distribution with both tails extending to infinity; 2, arithmetic mean, mode, and median identical; and 3, shape completely determined by the mean and standard deviation.
The discipline studying genetic composition of populations and effects of factors such as GENETIC SELECTION, population size, MUTATION, migration, and GENETIC DRIFT on the frequencies of various GENOTYPES and PHENOTYPES using a variety of GENETIC TECHNIQUES.
Statistical models of the production, distribution, and consumption of goods and services, as well as of financial considerations. For the application of statistics to the testing and quantifying of economic theories MODELS, ECONOMETRIC is available.
Substances used for their pharmacological actions on any aspect of neurotransmitter systems. Neurotransmitter agents include agonists, antagonists, degradation inhibitors, uptake inhibitors, depleters, precursors, and modulators of receptor function.
The probability that an event will occur. It encompasses a variety of measures of the probability of a generally unfavorable outcome.
Theoretical representations that simulate the behavior or activity of chemical processes or phenomena; includes the use of mathematical equations, computers, and other electronic equipment.
Number of individuals in a population relative to space.
The number of units (persons, animals, patients, specified circumstances, etc.) in a population to be studied. The sample size should be big enough to have a high likelihood of detecting a true difference between two groups. (From Wassertheil-Smoller, Biostatistics and Epidemiology, 1990, p95)
The basic cellular units of nervous tissue. Each neuron consists of a body, an axon, and dendrites. Their purpose is to receive, conduct, and transmit impulses in the NERVOUS SYSTEM.
The genetic constitution of the individual, comprising the ALLELES present at each GENETIC LOCUS.
A statistical technique that isolates and assesses the contributions of categorical independent variables to variation in the mean of a continuous dependent variable.
Studies in which a number of subjects are selected from all subjects in a defined population. Conclusions based on sample results may be attributed only to the population sampled.
Variant forms of the same gene, occupying the same locus on homologous CHROMOSOMES, and governing the variants in production of the same gene product.
Gated, ion-selective glycoproteins that traverse membranes. The stimulus for ION CHANNEL GATING can be due to a variety of stimuli such as LIGANDS, a TRANSMEMBRANE POTENTIAL DIFFERENCE, mechanical deformation or through INTRACELLULAR SIGNALING PEPTIDES AND PROTEINS.
Membrane-bound compartments which contain transmitter molecules. Synaptic vesicles are concentrated at presynaptic terminals. They actively sequester transmitter molecules from the cytoplasm. In at least some synapses, transmitter release occurs by fusion of these vesicles with the presynaptic membrane, followed by exocytosis of their contents.
The number of new cases of a given disease during a given period in a specified population. It also is used for the rate at which new events occur in a defined population. It is differentiated from PREVALENCE, which refers to all cases, new or old, in the population at a given time.
The ratio of alveolar ventilation to simultaneous alveolar capillary blood flow in any part of the lung. (Stedman, 25th ed)
The distal terminations of axons which are specialized for the release of neurotransmitters. Also included are varicosities along the course of axons which have similar specializations and also release transmitters. Presynaptic terminals in both the central and peripheral nervous systems are included.
The status during which female mammals carry their developing young (EMBRYOS or FETUSES) in utero before birth, beginning from FERTILIZATION to BIRTH.
The measure of that part of the heat or energy of a system which is not available to perform work. Entropy increases in all natural (spontaneous and irreversible) processes. (From Dorland, 28th ed)
Statistical models used in survival analysis that assert that the effect of the study factors on the hazard rate in the study population is multiplicative and does not change over time.
Blocking of the PULMONARY ARTERY or one of its branches by an EMBOLUS.
Any deviation of results or inferences from the truth, or processes leading to such deviation. Bias can result from several sources: one-sided or systematic variations in measurement from the true value (systematic error); flaws in study design; deviation of inferences, interpretations, or analyses based on flawed data or data collection; etc. There is no sense of prejudice or subjectivity implied in the assessment of bias under these conditions.
Summarizing techniques used to describe the pattern of mortality and survival in populations. These methods can be applied to the study not only of death, but also of any defined endpoint such as the onset of disease or the occurrence of disease complications.
The ability of a substrate to allow the passage of ELECTRONS.
A distribution function used to describe the occurrence of rare events or to describe the sampling distribution of isolated counts in a continuum of time or space.
The use of statistical and mathematical methods to analyze biological observations and phenomena.
The study of PHYSICAL PHENOMENA and PHYSICAL PROCESSES as applied to living things.
Maleness or femaleness as a constituent element or influence contributing to the production of a result. It may be applicable to the cause or effect of a circumstance. It is used with human or animal concepts but should be differentiated from SEX CHARACTERISTICS, anatomical or physiological manifestations of sex, and from SEX DISTRIBUTION, the number of males and females in given circumstances.
An object or a situation that can serve to reinforce a response, to satisfy a motive, or to afford pleasure.
In INFORMATION RETRIEVAL, machine-sensing or identification of visible patterns (shapes, forms, and configurations). (Harrod's Librarians' Glossary, 7th ed)
The process of cumulative change over successive generations through which organisms acquire their distinguishing morphological and physiological characteristics.
A range of values for a variable of interest, e.g., a rate, constructed so that this range has a specified probability of including the true value of the variable.
The application of STATISTICS to biological systems and organisms involving the retrieval or collection, analysis, reduction, and interpretation of qualitative and quantitative data.
Extensive collections, reputedly complete, of facts and data garnered from material of a specialized subject area and made available for analysis and application. The collection can be automated by various contemporary methods for retrieval. The concept should be differentiated from DATABASES, BIBLIOGRAPHIC which is restricted to collections of bibliographic references.
Positive test results in subjects who do not possess the attribute for which the test is conducted. The labeling of healthy persons as diseased when screening in the detection of disease. (Last, A Dictionary of Epidemiology, 2d ed)
Differential and non-random reproduction of different genotypes, operating to alter the gene frequencies within a population.
A phenotypically recognizable genetic trait which can be used to identify a genetic locus, a linkage group, or a recombination event.
A schedule prescribing when the subject is to be reinforced or rewarded in terms of temporal interval in psychological experiments. The schedule may be continuous or intermittent.
Period after successful treatment in which there is no appearance of the symptoms or effects of the disease.
Levels within a diagnostic group which are established by various measurement criteria applied to the seriousness of a patient's disorder.
Genotypic differences observed among individuals in a population.
The relationship between the dose of an administered drug and the response of the organism to the drug.
The ratio of two odds. The exposure-odds ratio for case control data is the ratio of the odds in favor of exposure among cases to the odds in favor of exposure among noncases. The disease-odds ratio for a cohort or cross section is the ratio of the odds in favor of disease among the exposed to the odds in favor of disease among the unexposed. The prevalence-odds ratio refers to an odds ratio derived cross-sectionally from studies of prevalent cases.
The proportion of one particular in the total of all ALLELES for one genetic locus in a breeding POPULATION.
Sodium channels found on salt-reabsorbing EPITHELIAL CELLS that line the distal NEPHRON; the distal COLON; SALIVARY DUCTS; SWEAT GLANDS; and the LUNG. They are AMILORIDE-sensitive and play a critical role in the control of sodium balance, BLOOD VOLUME, and BLOOD PRESSURE.
A plan for collecting and utilizing data so that desired information can be obtained with sufficient precision or so that an hypothesis can be tested properly.
Tumors or cancer of the human BREAST.
The process of cumulative change at the level of DNA; RNA; and PROTEINS, over successive generations.
Descriptions of specific amino acid, carbohydrate, or nucleotide sequences which have appeared in the published literature and/or are deposited in and maintained by databanks such as GENBANK, European Molecular Biology Laboratory (EMBL), National Biomedical Research Foundation (NBRF), or other sequence repositories.
Studies in which the presence or absence of disease or other health-related variables are determined in each member of the study population or in a representative sample at one particular time. This contrasts with LONGITUDINAL STUDIES which are followed over a period of time.
A nonparametric method of compiling LIFE TABLES or survival tables. It combines calculated probabilities of survival and estimates to allow for observations occurring beyond a measurement threshold, which are assumed to occur randomly. Time intervals are defined as ending each time an event occurs and are therefore unequal. (From Last, A Dictionary of Epidemiology, 1995)
Voltage-dependent cell membrane glycoproteins selectively permeable to calcium ions. They are categorized as L-, T-, N-, P-, Q-, and R-types based on the activation and inactivation kinetics, ion specificity, and sensitivity to drugs and toxins. The L- and T-types are present throughout the cardiovascular and central nervous systems and the N-, P-, Q-, & R-types are located in neuronal tissue.
A systematic collection of factual data pertaining to health and disease in a human population within a given geographic area.
The prediction or projection of the nature of future problems or existing conditions based upon the extrapolation or interpretation of existing scientific data or by the application of scientific methodology.
Investigative technique commonly used during ELECTROENCEPHALOGRAPHY in which a series of bright light flashes or visual patterns are used to elicit brain activity.
Studies in which variables relating to an individual or group of individuals are assessed over a period of time.
Statistical models in which the value of a parameter for a given value of a factor is assumed to be equal to a + bx, where a and b are constants. The models predict a linear regression.
An infant during the first month after birth.
The physical characteristics and processes of biological systems.
The relationships of groups of organisms as reflected by their genetic makeup.
A set of statistical methods used to group variables or observations into strongly inter-related subgroups. In epidemiology, it may be used to analyze a closely grouped series of events or cases of disease or other health-related phenomenon with well-defined distribution patterns in relation to time or place or both.
The worsening of a disease over time. This concept is most often used for chronic and incurable diseases where the stage of the disease is an important determinant of therapy and prognosis.
Electrical responses recorded from nerve, muscle, SENSORY RECEPTOR, or area of the CENTRAL NERVOUS SYSTEM following stimulation. They range from less than a microvolt to several microvolts. The evoked potential can be auditory (EVOKED POTENTIALS, AUDITORY), somatosensory (EVOKED POTENTIALS, SOMATOSENSORY), visual (EVOKED POTENTIALS, VISUAL), or motor (EVOKED POTENTIALS, MOTOR), or other modalities that have been reported.
Theory and development of COMPUTER SYSTEMS which perform tasks that normally require human intelligence. Such tasks may include speech recognition, LEARNING; VISUAL PERCEPTION; MATHEMATICAL COMPUTING; reasoning, PROBLEM SOLVING, DECISION-MAKING, and translation of language.
The record of descent or ancestry, particularly of a particular condition or trait, indicating individual family members, their relationships, and their status with respect to the trait or condition.
Predetermined sets of questions used to collect data - clinical data, social status, occupational group, etc. The term is often applied to a self-completed survey instrument.
A functional system which includes the organisms of a natural community together with their environment. (McGraw Hill Dictionary of Scientific and Technical Terms, 4th ed)
Theoretical representations that simulate psychological processes and/or social processes. These include the use of mathematical equations, computers, and other electronic equipment.
Social and economic factors that characterize the individual or group within the social structure.
A process that includes the determination of AMINO ACID SEQUENCE of a protein (or peptide, oligopeptide or peptide fragment) and the information analysis of the sequence.
Research techniques that focus on study designs and data gathering methods in human and animal populations.
The capacity of the NERVOUS SYSTEM to change its reactivity as the result of successive activations.
Non-invasive method of demonstrating internal anatomy based on the principle that atomic nuclei in a strong magnetic field absorb pulses of radiofrequency energy and emit them as radiowaves which can be reconstructed into computerized images. The concept includes proton spin tomographic techniques.
The science dealing with the earth and its life, especially the description of land, sea, and air and the distribution of plant and animal life, including humanity and human industries with reference to the mutual relations of these elements. (From Webster, 3d ed)
Linear POLYPEPTIDES that are synthesized on RIBOSOMES and may be further modified, crosslinked, cleaved, or assembled into complex proteins with several subunits. The specific sequence of AMINO ACIDS determines the shape the polypeptide will take, during PROTEIN FOLDING, and the function of the protein.
The arrangement of two or more amino acid or base sequences from an organism or organisms in such a way as to align areas of the sequences sharing common properties. The degree of relatedness or homology between the sequences is predicted computationally or statistically based on weights assigned to the elements aligned between the sequences. This in turn can serve as a potential indicator of the genetic relatedness between the organisms.
The co-inheritance of two or more non-allelic GENES due to their being located more or less closely on the same CHROMOSOME.
A technique of inputting two-dimensional images into a computer and then enhancing or analyzing the imagery into a form that is more useful to the human observer.
Computer-assisted interpretation and analysis of various mathematical functions related to a particular problem.
The strengthening of a conditioned response.
The total process by which organisms produce offspring. (Stedman, 25th ed)
Statistical interpretation and description of a population with reference to distribution, composition, or structure.
The transference of BONE MARROW from one human or animal to another for a variety of purposes including HEMATOPOIETIC STEM CELL TRANSPLANTATION or MESENCHYMAL STEM CELL TRANSPLANTATION.
The application of probability and statistical methods to calculate the risk of occurrence of any event, such as onset of illness, recurrent disease, hospitalization, disability, or death. It may include calculation of the anticipated money costs of such events and of the premiums necessary to provide for payment of such costs.
The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos.
Based on known statistical data, the number of years which any person of a given age may reasonably expected to live.
Any method used for determining the location of and relative distances between genes on a chromosome.
Ion channels that specifically allow the passage of SODIUM ions. A variety of specific sodium channel subtypes are involved in serving specialized functions such as neuronal signaling, CARDIAC MUSCLE contraction, and KIDNEY function.
Warm-blooded VERTEBRATES possessing FEATHERS and belonging to the class Aves.
Soluble protein fragments formed by the proteolytic action of plasmin on fibrin or fibrinogen. FDP and their complexes profoundly impair the hemostatic process and are a major cause of hemorrhage in intravascular coagulation and fibrinolysis.
Includes the spectrum of human immunodeficiency virus infections that range from asymptomatic seropositivity, thru AIDS-related complex (ARC), to acquired immunodeficiency syndrome (AIDS).
A computer architecture, implementable in either hardware or software, modeled after biological neural networks. Like the biological system in which the processing capability is a result of the interconnection strengths between arrays of nonlinear processing nodes, computerized neural networks, often called perceptrons or multilayer connectionist models, consist of neuron-like units. A homogeneous group of units makes up a layer. These networks are good at pattern recognition. They are adaptive, performing tasks by example, and thus are better for decision-making than are linear learning machines or cluster analysis. They do not require explicit programming.
A multistage process that includes cloning, physical mapping, subcloning, determination of the DNA SEQUENCE, and information analysis.
The actual costs of providing services related to the delivery of health care, including the costs of procedures, therapies, and medications. It is differentiated from HEALTH EXPENDITURES, which refers to the amount of money paid for the services, and from fees, which refers to the amount charged, regardless of cost.
Theoretical construct used in applied mathematics to analyze certain situations in which there is an interplay between parties that may have similar, opposed, or mixed interests. In a typical game, decision-making "players," who each have their own goals, try to gain advantage over the other parties by anticipating each other's decisions; the game is finally resolved as a consequence of the players' decisions.
The treatment of a disease or condition by several different means simultaneously or sequentially. Chemoimmunotherapy, RADIOIMMUNOTHERAPY, chemoradiotherapy, cryochemotherapy, and SALVAGE THERAPY are seen most frequently, but their combinations with each other and surgery are also used.
A class of statistical methods applicable to a large set of probability distributions used to test for correlation, location, independence, etc. In most nonparametric statistical tests, the original scores or observations are replaced by another variable containing less information. An important class of nonparametric tests employs the ordinal properties of the data. Another class of tests uses information about whether an observation is above or below some fixed value such as the median, and a third class is based on the frequency of the occurrence of runs in the data. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed, p1284; Corsini, Concise Encyclopedia of Psychology, 1987, p764-5)
Methods which attempt to express in replicable terms the extent of the neoplasm in the patient.
An interdisciplinary study dealing with the transmission of messages or signals, or the communication of information. Information theory does not directly deal with meaning or content, but with physical representations that have meaning or content. It overlaps considerably with communication theory and CYBERNETICS.
Systematic gathering of data for a particular purpose from various sources, including questionnaires, interviews, observation, existing records, and electronic devices. The process is usually preliminary to statistical analysis of the data.
Transplantation between individuals of the same species. Usually refers to genetically disparate individuals in contradistinction to isogeneic transplantation for genetically identical individuals.
Therapeutic act or process that initiates a response to a complete or partial remission level.
Disease having a short and relatively severe course.
New abnormal growth of tissue. Malignant neoplasms show a greater degree of anaplasia and have the properties of invasion and metastasis, compared to benign neoplasms.
Works about clinical trials that involve at least one test treatment and one control treatment, concurrent enrollment and follow-up of the test- and control-treated groups, and in which the treatments to be administered are selected by a random process, such as the use of a random-numbers table.
Application of computer programs designed to assist the physician in solving a diagnostic problem.
A curved elevation of GRAY MATTER extending the entire length of the floor of the TEMPORAL HORN of the LATERAL VENTRICLE (see also TEMPORAL LOBE). The hippocampus proper, subiculum, and DENTATE GYRUS constitute the hippocampal formation. Sometimes authors include the ENTORHINAL CORTEX in the hippocampal formation.
Models used experimentally or theoretically to study molecular shape, electronic properties, or interactions; includes analogous molecules, computer-generated graphics, and mechanical structures.
The capacity to conceive or to induce conception. It may refer to either the male or female.
The outward appearance of the individual. It is the product of interactions between genes, and between the GENOTYPE and the environment.
The sequence of PURINES and PYRIMIDINES in nucleic acids and polynucleotides. It is also called nucleotide sequence.
A statistical means of summarizing information from a series of measurements on one individual. It is frequently used in clinical pharmacology where the AUC from serum levels can be interpreted as the total uptake of whatever has been administered. As a plot of the concentration of a drug against time, after a single dose of medicine, producing a standard shape curve, it is a means of comparing the bioavailability of the same drug made by different companies. (From Winslade, Dictionary of Clinical Research, 1992)
The determination of the nature of a disease or condition, or the distinguishing of one disease or condition from another. Assessment may be made through physical examination, laboratory tests, or the likes. Computerized programs may be used to enhance the decision-making process.
Female germ cells derived from OOGONIA and termed OOCYTES when they enter MEIOSIS. The primary oocytes begin meiosis but are arrested at the diplotene state until OVULATION at PUBERTY to give rise to haploid secondary oocytes or ova (OVUM).
A major class of calcium activated potassium channels whose members are voltage-dependent. MaxiK channels are activated by either membrane depolarization or an increase in intracellular Ca(2+). They are key regulators of calcium and electrical signaling in a variety of tissues.
The production of offspring by selective mating or HYBRIDIZATION, GENETIC in animals or plants.
Tumors or cancer of the PROSTATE.
The total number of individuals inhabiting a particular region or area.
Recording of electric currents developed in the brain by means of electrodes applied to the scalp, to the surface of the brain, or placed within the substance of the brain.
The frequency of different ages or age groups in a given population. The distribution may refer to either how many or what proportion of the group. The population is usually patients with a specific disease but the concept is not restricted to humans and is not restricted to medicine.
An individual having different alleles at one or more loci regarding a specific character.
Parliamentary democracy located between France on the northeast and Portugual on the west and bordered by the Atlantic Ocean and the Mediterranean Sea.
The systems and processes involved in the establishment, support, management, and operation of registers, e.g., disease registers.
Organized periodic procedures performed on large groups of people for the purpose of detecting disease.
The local recurrence of a neoplasm following treatment. It arises from microscopic cells of the original neoplasm that have escaped therapeutic intervention and later become clinically visible at the original site.
Studies which start with the identification of persons with a disease of interest and a control (comparison, referent) group without the disease. The relationship of an attribute to the disease is examined by comparing diseased and non-diseased persons with regard to the frequency or levels of the attribute in each group.
A tetrameric calcium release channel in the SARCOPLASMIC RETICULUM membrane of SMOOTH MUSCLE CELLS, acting oppositely to SARCOPLASMIC RETICULUM CALCIUM-TRANSPORTING ATPASES. It is important in skeletal and cardiac excitation-contraction coupling and studied by using RYANODINE. Abnormalities are implicated in CARDIAC ARRHYTHMIAS and MUSCULAR DISEASES.
The clinical entity characterized by anorexia, diarrhea, loss of hair, leukopenia, thrombocytopenia, growth retardation, and eventual death brought about by the GRAFT VS HOST REACTION.
Potassium channels whose activation is dependent on intracellular calcium concentrations.
The mating of plants or non-human animals which are closely related genetically.

The significance of non-significance. (1/8370)

We discuss the implications of empirical results that are statistically non-significant. Figures illustrate the interrelations among effect size, sample sizes and their dispersion, and the power of the experiment. All calculations (detailed in Appendix) are based on actual noncentral t-distributions, with no simplifying mathematical or statistical assumptions, and the contribution of each tail is determined separately. We emphasize the importance of reporting, wherever possible, the a priori power of a study so that the reader can see what the chances were of rejecting a null hypothesis that was false. As a practical alternative, we propose that non-significant inference be qualified by an estimate of the sample size that would be required in a subsequent experiment in order to attain an acceptable level of power under the assumption that the observed effect size in the sample is the same as the true effect size in the population; appropriate plots are provided for a power of 0.8. We also point out that successive outcomes of independent experiments each of which may not be statistically significant on its own, can be easily combined to give an overall p value that often turns out to be significant. And finally, in the event that the p value is high and the power sufficient, a non-significant result may stand and be published as such.  (+info)

Capture-recapture models including covariate effects. (2/8370)

Capture-recapture methods are used to estimate the incidence of a disease, using a multiple-source registry. Usually, log-linear methods are used to estimate population size, assuming that not all sources of notification are dependent. Where there are categorical covariates, a stratified analysis can be performed. The multinomial logit model has occasionally been used. In this paper, the authors compare log-linear and logit models with and without covariates, and use simulated data to compare estimates from different models. The crude estimate of population size is biased when the sources are not independent. Analyses adjusting for covariates produce less biased estimates. In the absence of covariates, or where all covariates are categorical, the log-linear model and the logit model are equivalent. The log-linear model cannot include continuous variables. To minimize potential bias in estimating incidence, covariates should be included in the design and analysis of multiple-source disease registries.  (+info)

Model for bacteriophage T4 development in Escherichia coli. (3/8370)

Mathematical relations for the number of mature T4 bacteriophages, both inside and after lysis of an Escherichia coli cell, as a function of time after infection by a single phage were obtained, with the following five parameters: delay time until the first T4 is completed inside the bacterium (eclipse period, nu) and its standard deviation (sigma), the rate at which the number of ripe T4 increases inside the bacterium during the rise period (alpha), and the time when the bacterium bursts (mu) and its standard deviation (beta). Burst size [B = alpha(mu - nu)], the number of phages released from an infected bacterium, is thus a dependent parameter. A least-squares program was used to derive the values of the parameters for a variety of experimental results obtained with wild-type T4 in E. coli B/r under different growth conditions and manipulations (H. Hadas, M. Einav, I. Fishov, and A. Zaritsky, Microbiology 143:179-185, 1997). A "destruction parameter" (zeta) was added to take care of the adverse effect of chloroform on phage survival. The overall agreement between the model and the experiment is quite good. The dependence of the derived parameters on growth conditions can be used to predict phage development under other experimental manipulations.  (+info)

Molecular studies suggest that cartilaginous fishes have a terminal position in the piscine tree. (4/8370)

The Chondrichthyes (cartilaginous fishes) are commonly accepted as being sister group to the other extant Gnathostomata (jawed vertebrates). To clarify gnathostome relationships and to aid in resolving and dating the major piscine divergences, we have sequenced the complete mtDNA of the starry skate and have included it in phylogenetic analysis along with three squalomorph chondrichthyans-the common dogfish, the spiny dogfish, and the star spotted dogfish-and a number of bony fishes and amniotes. The direction of evolution within the gnathostome tree was established by rooting it with the most closely related non-gnathostome outgroup, the sea lamprey, as well as with some more distantly related taxa. The analyses placed the chondrichthyans in a terminal position in the piscine tree. These findings, which also suggest that the origin of the amniote lineage is older than the age of the oldest extant bony fishes (the lungfishes), challenge the evolutionary direction of several morphological characters that have been used in reconstructing gnathostome relationships. Applying as a calibration point the age of the oldest lungfish fossils, 400 million years, the molecular estimate placed the squalomorph/batomorph divergence at approximately 190 million years before present. This dating is consistent with the occurrence of the earliest batomorph (skates and rays) fossils in the paleontological record. The split between gnathostome fishes and the amniote lineage was dated at approximately 420 million years before present.  (+info)

Toward a leukemia treatment strategy based on the probability of stem cell death: an essay in honor of Dr. Emil J Freireich. (5/8370)

Dr. Emil J Freireich is a pioneer in the rational treatment of cancer in general and leukemia in particular. This essay in his honor suggests that the cell kill concept of chemotherapy of acute myeloblastic leukemia be extended to include two additional ideas. The first concept is that leukemic blasts, like normal hemopoietic cells, are organized in hierarchies, headed by stem cells. In both normal and leukemic hemopoiesis, killing stem cells will destroy the system; furthermore, both normal and leukemic cells respond to regulators. It follows that acute myelogenous leukemia should be considered as a dependent neoplasm. The second concept is that cell/drug interaction should be considered as two phases. The first, or proximal phase, consists of the events that lead up to injury; the second, or distal phase, comprises the responses of the cell that contribute to either progression to apoptosis or recovery. Distal responses are described briefly. Regulated drug sensitivity is presented as an example of how distal responses might be used to improve treatment.  (+info)

A reanalysis of IgM Western blot criteria for the diagnosis of early Lyme disease. (6/8370)

A two-step approach for diagnosis of Lyme disease, consisting of an initial EIA followed by a confirmatory Western immunoblot, has been advised by the Centers for Disease Control and Prevention (CDC). However, these criteria do not examine the influence of the prior probability of Lyme disease in a given patient on the predictive value of the tests. By using Bayesian analysis, a mathematical algorithm is proposed that computes the probability that a given patient's Western blot result represents Lyme disease. Assuming prior probabilities of early Lyme disease of 1%-10%, the current CDC minimum criteria for IgM immunoblot interpretation yield posttest probabilities of 4%-32%. The value of the two-step approach for diagnosis of early Lyme disease may be limited in populations at lower risk of disease or when patients present with atypical signs and symptoms.  (+info)

Bayesian inference on biopolymer models. (7/8370)

MOTIVATION: Most existing bioinformatics methods are limited to making point estimates of one variable, e.g. the optimal alignment, with fixed input values for all other variables, e.g. gap penalties and scoring matrices. While the requirement to specify parameters remains one of the more vexing issues in bioinformatics, it is a reflection of a larger issue: the need to broaden the view on statistical inference in bioinformatics. RESULTS: The assignment of probabilities for all possible values of all unknown variables in a problem in the form of a posterior distribution is the goal of Bayesian inference. Here we show how this goal can be achieved for most bioinformatics methods that use dynamic programming. Specifically, a tutorial style description of a Bayesian inference procedure for segmentation of a sequence based on the heterogeneity in its composition is given. In addition, full Bayesian inference algorithms for sequence alignment are described. AVAILABILITY: Software and a set of transparencies for a tutorial describing these ideas are available at http://www.wadsworth.org/res&res/bioinfo/  (+info)

Using imperfect secondary structure predictions to improve molecular structure computations. (8/8370)

MOTIVATION: Until ab initio structure prediction methods are perfected, the estimation of structure for protein molecules will depend on combining multiple sources of experimental and theoretical data. Secondary structure predictions are a particularly useful source of structural information, but are currently only approximately 70% correct, on average. Structure computation algorithms which incorporate secondary structure information must therefore have methods for dealing with predictions that are imperfect. EXPERIMENTS PERFORMED: We have modified our algorithm for probabilistic least squares structural computations to accept 'disjunctive' constraints, in which a constraint is provided as a set of possible values, each weighted with a probability. Thus, when a helix is predicted, the distances associated with a helix are given most of the weight, but some weights can be allocated to the other possibilities (strand and coil). We have tested a variety of strategies for this weighting scheme in conjunction with a baseline synthetic set of sparse distance data, and compared it with strategies which do not use disjunctive constraints. RESULTS: Naive interpretations in which predictions were taken as 100% correct led to poor-quality structures. Interpretations that allow disjunctive constraints are quite robust, and even relatively poor predictions (58% correct) can significantly increase the quality of computed structures (almost halving the RMS error from the known structure). CONCLUSIONS: Secondary structure predictions can be used to improve the quality of three-dimensional structural computations. In fact, when interpreted appropriately, imperfect predictions can provide almost as much improvement as perfect predictions in three-dimensional structure calculations.  (+info)

Definition of pretest probability in the Financial Dictionary - by Free online English dictionary and encyclopedia. What is pretest probability? Meaning of pretest probability as a finance term. What does pretest probability mean in finance?
This paper presents a probabilistic approach to model the problem of power supply voltage fluctuations. Error probability calculations are shown for some 90-nm technology digital circuits. The analysis here considered gives the timing violation error probability as a new design quality factor in front of conventional techniques that assume the full perfection of the circuit. The evaluation of the error bound can be useful for new design paradigms where retry and self-recovering techniques are being applied to the design of high performance processors. The method here described allows to evaluate the performance of these techniques by means of calculating the expected error probability in terms of power supply distribution quality ...
Conditional probability refers to the probability of a generic event, given some extra information. More specifically, the conditional probability of one event A with respect to B: Expresses the probability of A given that B has occurred. If the two events are independent, the simple and conditional probability coincides (the occurrence of B has nothing…
If your friend tells you that an even number showed up, what is the probability that you rolled a 5? It cant happen since 5 is an odd number.. So what is happening in these cases? Well, you are learning some additional information that leads us to change the probability of an event occurring. In effect, knowing additional information changes the sample size we use to compute the probabilities. Therefore, the probability of our event occurring must change.. The notation P(F│E) means the probability of F occurring given that (or knowing that) event E already occurred. For the above dice example, F = {roll a 5}, and E = {result is an odd number}, and we found that P(F│E) = 33.33%.. Conditional probabilities are useful when presented with data that comes in tables, where different categories of data (say, Male and Female), are broken down into additional sub-categories (say, marriage status).. To compute the probabilities of dependent data, we use the Conditional Probability Rule. In ...
TY - JOUR. T1 - Conditional probability of survival in patients with newly diagnosed glioblastoma. AU - Polley, Mei Yin C.. AU - Lamborn, Kathleen R.. AU - Chang, Susan M.. AU - Butowski, Nicholas. AU - Clarke, Jennifer L.. AU - Prados, Michael. PY - 2011/11/1. Y1 - 2011/11/1. N2 - Purpose: The disease outcome for patients with cancer is typically described in terms of estimated survival from diagnosis. Conditional probability offers more relevant information regarding survival for patients once they have survived for some time. We report conditional survival probabilities on the basis of 498 patients with glioblastoma multiforme receiving radiation and chemotherapy. For 1-year survivors, we evaluated variables that may inform subsequent survival. Motivated by the trend in data, we also evaluated the assumption of constant hazard. Patients and Methods: Patients enrolled onto seven phase II protocols between 1975 and 2007 were included. Conditional survival probabilities and 95% CIs were ...
Conditional probability is the probability of an event occurring given that another event has already occurred. The concept is one of the quintessential concepts in probability theoryTotal Probability RuleThe Total Probability Rule (also known as the law of total probability) is a fundamental rule in statistics relating to conditional and marginal. Note that conditional probability…
View Notes - Slides7_v1 from ECON 404 at University of Michigan. Sampling Distributions Utku Suleymanoglu UMich Utku Suleymanoglu (UMich) Sampling Distributions 1 / 21 Introduction Population
Pretest probability (PTP) assessment plays a central role in diagnosis. This report compares a novel attribute-matching method to generate a PTP for acute coronary syndrome (ACS). We compare the new method with a validated logistic regression equation (LRE). Eight clinical variables (attributes) were chosen by classification and regression tree analysis of a prospectively collected reference database of 14,796 emergency department (ED) patients evaluated for possible ACS. For attribute matching, a computer program identifies patients within the database who have the exact profile defined by clinician input of the eight attributes. The novel method was compared with the LRE for ability to produce PTP estimation |2% in a validation set of 8,120 patients evaluated for possible ACS and did not have ST segment elevation on ECG. 1,061 patients were excluded prior to validation analysis because of ST-segment elevation (713), missing data (77) or being lost to follow-up (271). In the validation set, attribute
that is a probability measure defined on a Radon space endowed with the Borel sigma-algebra) and a real-valued random variable T. As discussed above, in this case there exists a regular conditional probability with respect to T. Moreover, we can alternatively define the regular conditional probability for an event A given a particular value t of the random variable T in the following manner:. ...
CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): This paper presents an application of recurrent networks for phone probability estimation in large vocabulary speech recognition. The need for efficient exploitation of context information is discussed
Methods and apparatus, including computer program products, for detecting an object in an image. The techniques include scanning a sequence of pixels in the image, each pixel having one or more property values associated with properties of the pixel, and generating a dynamic probability value for each of one or more pixels in the sequence. The dynamic probability value for a given pixel represents a probability that the given pixel has neighboring pixels in the sequence that correspond to one or more features of the object. The dynamic probability value is generated by identifying a dynamic probability value associated with a pixel that immediately precedes the given pixel in the sequence; updating the identified dynamic probability value based on the property values of the immediately preceding pixel; and associating the updated probability value with the given pixel.
Bivariate multinomial data such as the left and right eyes retinopathy status data are analyzed either by using a joint bivariate probability model or by exploiting certain odds ratio-based association models. However, the joint bivariate probability model yields marginal probabilities, which are complicated functions of marginal and association parameters for both variables, and the odds ratio-based association model treats the odds ratios involved in the joint probabilities as working parameters, which are consequently estimated through certain arbitrary working regression models. Also, this later odds ratio-based model does not provide any easy interpretations of the correlations between two categorical variables. On the basis of pre-specified marginal probabilities, in this paper, we develop a bivariate normal type linear conditional multinomial probability model to understand the correlations between two categorical variables. The parameters involved in the model are consistently estimated
For this problem, we know $p=0.43$ and $n=50$. First, we should check our conditions for the sampling distribution of the sample proportion.. \(np=50(0.43)=21.5\) and \(n(1-p)=50(1-0.43)=28.5\) - both are greater than 5.. Since the conditions are satisfied, $\hat{p}$ will have a sampling distribution that is approximately normal with mean \(\mu=0.43\) and standard deviation [standard error] \(\sqrt{\dfrac{0.43(1-0.43)}{50}}\approx 0.07\).. \begin{align} P(0.45,\hat{p},0.5) &=P\left(\frac{0.45-0.43}{0.07}, \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}},\frac{0.5-0.43}{0.07}\right)\\ &\approx P\left(0.286,Z,1\right)\\ &=P(Z,1)-P(Z,0.286)\\ &=0.8413-0.6126\\ &=0.2287\end{align}. Therefore, if the true proportion of American who own an iPhone is 43%, then there would be a 22.87% chance that we would see a sample proportion between 45% and 50% when the sample size is 50.. ...
I would like to know if the following inequality is satisfied by all probability distributions (or at least some class of probability distributions) for all integer $n \geq 2$. $\int_0^{\infty} F(z)^{n-1}(1-\frac{F(z)}{n})\left[zF(z)^{n-2} - \int_0^z F(t)^{n-2}dt\right]f(z)dz$ $\leq \int_0^{\infty} F(z)^{n-1}\left[zF(z)^{n-1} - \int_0^z F(t)^{n-1}dt\right]f(z)dz $. Some comments follow:. 1) F(z) is the cumulative distribution function of any probability distribution over positive real numbers. The outer integral runs over the entire support of the distribution, thus, in general, from zero to infinity. f(z) is the probability density function. 2) I will be happy even if this is proved for bounded support distributions, in which case, the outer integral runs from 0 to some upper limit H.. 3) Note that both the LHS and the RHS are always non-negative. This is because of the special form of what is inside the square brackets. For both the LHS and the RHS, the second term in the square bracket (i.e. ...
Let X, Y be independent, standard normal random variables, and let U = X + Y and V = X - Y. (a) Find the joint probability density function of (U, V) and specify its domain. (b) Find the marginal probability density function of U.
In this paper, new probability estimates are derived for ideal lattice codes from totally real number fields using ideal class Dedekind zeta functions. In contrast to previous work on the subject, it is not assumed that the ideal in question is principal. In particular, it is shown that the corresponding inverse norm sum depends not only on the regulator and discriminant of the number field, but also on the values of the ideal class Dedekind zeta functions. Along the way, we derive an estimate of the number of elements in a given ideal with a certain algebraic norm within a finite hypercube. We provide several examples which measure the accuracy and predictive ability of our theorems.
Probabilistic reasoning is essential for operating sensibly and optimally in the 21st century. However, research suggests that students have many difficulties in understanding conditional probabilities and that Bayesian-type problems are replete with misconceptions such as the base rate fallacy and confusion of the inverse. Using a dynamic pachinkogram, a visual representation of the traditional probability tree, we explore six undergraduate probability students reasoning processes as they interact with this tool. Initial findings suggest that in simulating a screening situation, the ability to vary the branch widths of the pachinkogram may have the potential to convey the impact of the base rate. Furthermore, we conjecture that the representation afforded by the pachinkogram may help to clarify the distinction between probabilities with inverted conditions ...
TY - JOUR. T1 - Velocity probability distribution scaling in wall-bounded flows at high Reynolds numbers. AU - Ge, M. W.. AU - Yang, Xiang I.A.. AU - Marusic, Ivan. PY - 2019/3. Y1 - 2019/3. N2 - Probability density functions (PDFs) give well-rounded statistical descriptions of stochastic quantities and therefore are fundamental to turbulence. Wall-bounded turbulent flows are of particular interest given their prevalence in a vast array of applications, but for these flows the scaling of velocity probability distribution is still far from being well founded. By exploiting the self-similarity in wall-bounded turbulent flows and modeling velocity fluctuations as results of self-repeating processes, we present a theoretical argument, supported by empirical evidence, for a universal velocity PDF scaling in high-Reynolds-number wall turbulence.. AB - Probability density functions (PDFs) give well-rounded statistical descriptions of stochastic quantities and therefore are fundamental to turbulence. ...
The Probability Calculator in Fidelitys Active Trader Pro can help you to determine the probability of an underlying equity or index trading above, below, or between certain price targets on a specified date.
A common problem is to determine by an elicitation process the parameters of a subjective distribution in a location-scale family. One method is to elicit assessments of the median and one other quartile, equate the assessed median to the location parameter, and estimate the scale from the difference. In a second method, all three quartiles are elicited and then the scale is estimated from the interquartile range. With either method, the location and scale estimates are not made independently. These methods are here studied by introducing probability models for the elicitation process itself. It is shown that the second (full-quartiles) method has important advantages not held by the first.. ...
Dear Nico, I would go logistic in that instance (however, take a look at what others do in your research field for managing the same issues). Kindest Regards, Carlo -----Messaggio originale----- Da: [email protected] [mailto:[email protected]] Per conto di [email protected] Inviato: giovedì 21 luglio 2011 23.20 A: Carlo Lazzaro; [email protected] Oggetto: st: Re: conditional probability , Thanks Carlo, but if I want to consider also some personal , characteristics (age, gender, ect). How I can estimate these probability? , is it enough a simple probit or logit? , thanks again , Nico , , 2011/7/19 Carlo Lazzaro ,[email protected],: ,, Nico wrote: ,, and prob(B,H) is the jointly probability to hiring a black worker ,, conditional on being a H worker ,, ,, ,, High skilled Low skilled Total ,, ---------------------------------------------- ,, Black 20 40 60 ,, ,, Others 30 50 80 ,, ---------------------------------------------- ,, Total 50 90 ...
As @Aksakal says, there is nothing weird about this: it is easy to see that the significance level (for a continuous random variable) is equal to the probability of a type I error. So your one-sided and two sided test have the same type I error probability. What differs is the power of the two tests. If you know that the alternative is an increase, then for the same type I error probability, the type II error probability is lower with the one sided test (or the power is higher). In fact, it can be shown that, for a given type I error probability (and in the univariate case), the one sided test is the most powerfull you can find, whatever the alternative is. This is thus the UMPT, the Uniformly Most Powerful Test. It all depends on what you want to test. Assume you want to buy lamps from your supplier and the supplier says that the life time of a lamp is 1000 hours (on average). If you want to test these lamps then you will probably not care if these lamps live longer so you will test $H_0: ...
Algebra 1 answers to Chapter 12 - Data Analysis and Probability - Concept Byte - Conditional Probability - Page 771 2 including work step by step written by community members like you. Textbook Authors: Hall, Prentice, ISBN-10: 0133500403, ISBN-13: 978-0-13350-040-0, Publisher: Prentice Hall
Definition: If the probability of any event depends on the occurrence of some other event then, it is called conditional probability. Formula of conditional....
Warren Buffett considers one basic principle, elementary probability, the core of his investing philosophy, helping him to identify tremendous stock opportunities.
One of the factors known to affect target detection is target probability. It is clear, though, that target probability can be manipulated in different ways. Here, in order to more accurately characterize the effects of target probability on frontal engagement, we examined the effects of two commonly-used but different target probability manipulations on neural activity. We found that manipulations that affected global stimulus class probability had a pronounced effect on ventrolateral prefrontal cortex and the insula, an effect which was absent with manipulations that only affected the likelihood of specific target stimuli occurring. This latter manipulation only modulated activity in dorsolateral prefrontal cortex and the precentral sulcus. Our data suggest two key points. First, different types of target probability have different neural consequences, and may therefore be very different in nature. Second, the data indicate that ventral and dorsal portions of prefrontal cortex respond to ...
Using a tree diagram to work out a conditional probability question. If someone fails a drug test, what is the probability that they actually are taking drugs?
Definition of prior probability: Probability that a certain event or outcome will occur. For example, economists may believe there is an 80% probability that the economy will grow by more than 2% in the coming year. Prior probability ...
NMath Stats from CenterSpace Software is a .NET class library that provides functions for statistical computation and biostatistics, including descriptive statistics, probability distributions, combinatorial functions, multiple linear regression, hypothesis testing, analysis of variance, and multivariate statistics.. NMath Stats provides classes for computing the probability density function (PDF), the cumulative distribution function (CDF), the inverse cumulative distribution function, and random variable moments for a variety of probability distributions, including beta, binomial, chi-square, exponential, F, gamma, geometric, logistic, log-normal, negative binomial, normal (Gaussian), Poisson, Students t, triangular, and Weibull distributions. The distribution classes share a common interface, so once you learn how to use one distribution class, its easy to use any of the others. This functionality can be used from any .NET language including VB.NET and F#.. The NMath Stats library is part ...
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I was under the impression that the uncertain state block within the robust control toolbox was the direction to go, but so far I havent been able to decipher the help information to learn how to use and apply it. (And as far as I can understand, it would be ideal b/c I can also run the model varying all the uncertain variables a certain number of times from the command line ...
Download free e-book on error probability in AWGN for BPSK, QPSK, 4-PAM, 16QAM, 16PSK and more. Matlab/Octave simulation models provided.
Download free e-book on error probability in AWGN for BPSK, QPSK, 4-PAM, 16QAM, 16PSK and more. Matlab/Octave simulation models provided.
the extent to which ordnance will miss the target A Gulf War usage, from the illustration by concentric rings on a chart: There was something called circular error probability, which simply meant the area where a bomb or missile was…
Expressions for the error probabilities in the detection of binary coherent orthogonal equienergy optical signals of random phase in thermal background noi
Prior probability distribution: lt;div class=hatnote|>Not to be confused with |a priori probability|.| |||||||||This article in... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled.
CiteSeerX - Scientific documents that cite the following paper: Base-calling of automated sequencer traces using phred. II. error probabilities
Sankhya: The Indian Journal of Statistics. 2001, Volume 63, Series B, Pt. 3, pp. 251--269. UNIFIED BAYESIAN AND CONDITIONAL FREQUENTIST TESTING FOR DISCRETE DISTRIBUTIONS. By. SARAT C. DASS, Michigan State University. SUMMARY. Testing of hypotheses for discrete distributions is considered in this paper. The goal is to develop conditional frequentist tests that allow the reporting of data-dependent error probabilities such that the error probabilities have a strict frequentist interpretation and also reflect the actual amount of evidence in the observed data. The resulting randomized tests are also seen to be Bayesian tests, in the strong sense that the reported error probabilities are also the posterior probabilities of the hypotheses. The new procedure is illustrated for a variety of testing situations, both simple and composite, involving discrete distributions. Testing linkage heterogeneity with the new procedure is given as an illustrative example.. AMS (1991) subject classification. ...
View Notes - Normal rvs_bb from BUS 45730 at Carnegie Mellon. THE NORMAL DISTRIBUTION, OTHER CONTINUOUS DISTRIBUTIONS, AND SAMPLING DISTRIBUTION 1. In its standardized form, the normal distribution
Mode: for a discrete random variable, the value with highest probability (the location at which the probability mass function has its peak); for a continuous random variable, the location at which the probability density function has its peak ...
Downloadable! This paper introduces a new technique to infer the risk-neutral probability distribution of an asset from the prices of options on this asset. The technique is based on using the trading volume of each option as a proxy of the informativeness of the option. Not requiring the implied probability distribution to recover exactly the market prices of the options allows us to weight each option by a function of its trading volume. As a result, we obtain implied probability distributions that are both smoother and should be more reflective of fundamentals.
We present an algorithm for pulse width estimation from blurred and nonlinear observations in the presence of signal dependent noise. The main application is the accurate measurement of image sizes on film. The problem is approached by modeling the signal as a discrete position finite state Markov process, and then determining the transition location that maximizes the a posteriori probability. It turns out that the blurred signal can be represented by a trellis, and the maximum a posteriori probability (MAP) estimation is obtained by finding the minimum cost path through the trellis. The latter is done by the Viterbi algorithm. Several examples are presented. These include the measurement of the width of a road in an aerial photo taken at an altitude of 5000 ft. The resulting width estimate is accurate to within a few inches.. © 1978 Optical Society of America. Full Article , PDF Article ...
Module 2: Probability, Random Variables & Probability Distributions Module 2b . Random Variable. What is a random variable? When experiments lead to categorical results, we assign numbers to the random variable: e.g., defective = 0, functional = 1 Why do we assign numbers?...
海词词典,最权威的学习词典,专业出版probability distribution law是什么意思,probability distribution law的用法,probability distribution law翻译和读音等详细讲解。海词词典:学习变容易,记忆很深刻。
This activity demonstrates the probability of an event happening with the simulation of a coin toss. Students will learn how probabilities can be computed. They will simulate distributions to check the reasonableness of the results. They also explore various probability distributions.
The Lovász Local Lemma (or LLL) concerns itself with the probability of avoiding a collection of bad events A, given that the set of events is nearly independent (each bad event A ∈ A has probability which is bounded above in terms of the number of other events A, A, etc. from which it is not independent), there is a non-zero probability of avoiding all of the bad events simultaneously. The original presentation seems to be the Lemma on page 8 of this pdf (the link to which can be found on Wikipedias page on the LLL); several other papers present it in a similar fashion.. In the article [arXiv:0903.0544], restricting to the setting where the bad events of the LLL are defined in terms of a probability space of independently distributed bits, Moser and Tardos present a probabilistic algorithm for sampling from the event space until an event is found which avoids all bad events, which requires at most polynomially many samples with high probability. However, their characterization of ...
Video created by Duke University for the course Behavioral Finance. Welcome to the second week. In this session, we will discover how our minds are inclined to distort probabilities, and either underestimate or overestimate the likelihood of ...
Compute the probability density function (PDF) for the chi-square distribution, given the degrees of freedom and the point at which to evaluate the function x. The chi-square distribution PDF identifies the relative likelihood that an associated random variable will have a particular value, and is very useful for analytics studies that consider chi-square distribution probabilities.
Objective: The objective of this study is to develop Human Error Probability model considering various internal and external factors affecting the seafarers performance.Background: Maintenance operations on-board ships are highly demanding. Maintenanceoperations are intensive activities requiring high man-machine interactions in challenging and evolving conditions. The evolving conditions are weather conditions, workplace temperature, ship motion, noise and vibration and workload and stress. For example, extreme weather condition affects the seafarers performance hence increasing the chances of error and consequently, can cause injuries or fatalities to personnel. An effective human error probability model is required to better manage maintenance on board ships. The developed model would assist in developing and maintaining effective risk management protocols.Method: The human error probability model is developed using probability theory applied to Bayesian Network. The model is tested using ...
Bayes theorem is a probability principle set forth by the English mathematician Thomas Bayes (1702-1761). Bayes theorem is of value in medical decision-making and some of the biomedical sciences. Bayes theorem is employed in clinical epidemiology to determine the probability of a particular disease in a group of people with a specific characteristic on the basis of the overall rate of that disease and of the likelihood of that specific characteristic in healthy and diseased individuals, respectively. A common application of Bayes theorem is in clinical decision making where it is used to estimate the probability of a particular diagnosis given the appearance of specific signs, symptoms, or test outcomes. For example, the accuracy of the exercise cardiac stress test in predicting significant coronary artery disease (CAD) depends in part on the pre-test likelihood of CAD: the prior probability in Bayes theorem. In technical terms, in Bayes theorem the impact of new data on the merit of ...
Calibrated probability assessments are subjective probabilities assigned by individuals who have been trained to assess probabilities in a way that historically represents their uncertainty. In other words, when a calibrated person says they are 80% confident in each of 100 predictions they made, they will get about 80% of them correct. Likewise, they will be right 90% of the time they say they are 90% certain, and so on. Calibration training improves subjective probabilities because most people are either overconfident or under-confident (usually the former). By practicing with a series of trivia questions, it is possible for subjects to fine-tune their ability to assess probabilities. For example, a subject may be asked: True or False: A hockey puck fits in a golf hole Confidence: Choose the probability that best represents your chance of getting this question right... 50% 60% 70% 80% 90% 100% If a person has no idea whatsoever, they will say they are only 50% confident. If they are ...
National security is one of many fields where public officials offer imprecise probability assessments when evaluating high-stakes decisions. This practice is often justified with arguments about how quantifying subjective judgments would bias analysts and decision makers toward overconfident action. We translate these arguments into testable hypotheses, and evaluate their validity through survey experiments involving national security professionals.
For two-class classification, it is common to classify by setting a threshold on class probability estimates, where the threshold is determined by {ROC} curve analysis. An analog for multi-class classification is learning a new class partitioning of the multiclass probability simplex to minimize empirical misclassification costs. We analyze the interplay between systematic errors in the class probability estimates and cost matrices for multi-class classification. We explore the effect on the class partitioning of five different transformations of the cost matrix. Experiments on benchmark datasets with naive Bayes and quadratic discriminant analysis show the effectiveness of learning a new partition matrix compared to previously proposed methods.
In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events. For instance, if the random variable X is used to denote the outcome of a coin toss (the experiment), then the probability distribution of X would take the value 0.5 for X = heads, and 0.5 for X = tails (assuming the coin is fair). Examples of random phenomena can include the results of an experiment or survey. A probability distribution is specified in terms of an underlying sample space, which is the set of all possible outcomes of the random phenomenon being observed. The sample space may be the set of real numbers or a set of vectors, or it may be a list of non-numerical values; for example, the sample space of a coin flip would be {heads, tails} . Probability distributions ...
This section will establish the groundwork for Bayesian Statistics. Probability, Random Variables, Means, Variances, and the Bayes Theorem will all be discussed. Bayes Theorem Bayes theorem is associated with probability statements that relate conditional and marginal properties of two random events. These statements are often written in the form the probability of A, given B and denoted P(A,B) = P(B,A)*P(A)/P(B) where P(B) not equal to 0. P(A) is often known as the Prior Probability (or as the Marginal Probability) P(A,B) is known as the Posterior Probability (Conditional Probability) P(B,A) is the conditional probability of B given A (also known as the likelihood function) P(B) is the prior on B and acts as the normalizing constant. In the Bayesian framework, the posterior probability is equal to the prior belief on A times the likelihood function given by P(B,A). Media:Mario.jpg ...
This section will establish the groundwork for Bayesian Statistics. Probability, Random Variables, Means, Variances, and the Bayes Theorem will all be discussed. Bayes Theorem Bayes theorem is associated with probability statements that relate conditional and marginal properties of two random events. These statements are often written in the form the probability of A, given B and denoted P(A,B) = P(B,A)*P(A)/P(B) where P(B) not equal to 0. P(A) is often known as the Prior Probability (or as the Marginal Probability) P(A,B) is known as the Posterior Probability (Conditional Probability) P(B,A) is the conditional probability of B given A (also known as the likelihood function) P(B) is the prior on B and acts as the normalizing constant. In the Bayesian framework, the posterior probability is equal to the prior belief on A times the likelihood function given by P(B,A). ...
We study asynchronous SSMA communication systems using binary spreading sequences of Markov chains and prove the CLT (central limit theorem) for the empirical distribution of the normalized MAI (multiple-access interference). We also prove that the distribution of the normalized MAI for asynchronous systems can never be Gaussian if chains are irreducible and aperiodic. Based on these results, we propose novel theoretical evaluations of bit error probabilities in such systems based on the CLT and compare these and conventional theoretical estimations based on the SGA (standard Gaussian approximation) with experimental results. Consequently we confirm that the proposed theoretical evaluations based on the CLT agree with the experimental results better than the theoretical evaluations based on the SGA. Accordingly, using the theoretical evaluations based on the CLT, we give the optimum spreading sequences of Markov chains in terms of bit error probabilities. ...
The author provides a stepwise approach for evaluating the results of fitting probability models to data as the focus for the book . . . . All this is packaged very systematically . . . . the booklet is highly successful in showing how probability models can be interpreted.. --Technometrics. Tim Futing Liaos Interpreting Probability Models. . . is an advanced text . . . . Liaos text is more theoretical, but is well exemplified using case studies . . . . this is a text for the more advanced statistician or the political scientist with strong leanings in this direction!. --John G. Taylor in Technology and Political Science What is the probability that something will occur, and how is that probability altered by a change in some independent variable? Aimed at answering these questions, Liao introduces a systematic way for interpreting a variety of probability models commonly used by social scientists. Since much of what social scientists study are measured in noncontinuous ways and thus cannot ...
How can it be useful in determining whether events actually transpired in the past, that is, when the sample field itself consists of what has already occurred (or not occurred) and when B is the probability of it having happened?. Statements like this (and its ilk; there are at least 3 of them in Hoffmans quotes) demonstrate a complete lack of understanding of both probability and Bayes theorem. Heres a real-world, routine application of Bayes theorem in medicine (it was in my probability textbook in college, although the disease wasnt specified): Lets say 1% of the population is HIV+. Furthermore, HIV antibody tests have a 1% false positive rate (which used to be true, but now its much lower) and a 0.1% false negative rate (this number is not so important). If you take an HIV test and the result is positive, what is the probability that you actually have the disease? Using Bayes theorem, one gets around 50%. Note that were not talking about future possibilities here - you either ...
The computed transition probability matrix reflects the characteristics of the particular sequence of observed facies employed in the computation. These particular characteristics may diverge somewhat from the expected sequence characteristics for a region. For example, a transition from facies A to facies B may never occur in the selected core, although it is known to occur elsewhere in the study area. To overcome this shortcoming, Kipling allows the user to modify the computed TPM to better match geological expectations. This is accomplished simply by editing the entries in the matrix. Because the modified facies membership probabilities are linked by formulas to the transition probability matrix, any changes to this matrix will automatically be reflected in the modified probabilities and facies predictions, and also in any existing plots of those values. This allows you to easily investigate the influence of the transition probability values on the sequence of predicted facies. Previous ...
This program covers the important topic Bayes Theorem in Probability and Statistics. We begin by discussing what Bayes Theorem is and why it is important. Next, we solve several problems that involve the essential ideas of Bayes Theorem to give students practice with the material. The entire lesson is taught by working example problems beginning with the easier ones and gradually progressing to the harder problems. Emphasis is placed on giving students confidence in their skills by gradual repetition so that the skills learned in this section are committed to long-term memory. (TMW Media Group, USA)
In the situation where hypothesis H explains evidence E, Pr(E,H) basically becomes a measure of the hypothesiss explanatory power. Pr(H,E) is called the posterior probability of H. Pr(H) is the prior probability of H, and Pr(E) is the prior probability of the evidence (very roughly, a measure of how surprising it is that wed find the evidence). Prior probabilities are probabilities relative to background knowledge, e.g. Pr(E) is the likelihood that wed find evidence E relative to our background knowledge. Background knowledge is actually used throughout Bayes theorem however, so we could view the theorem this way where B is our background knowledge ...
Part One. Descriptive Statistics. 1. Introduction to Statistics. 1.1. An Overview of Statistics. 1.2. Data Classification. 1.3. Data Collection and Experimental Design. 2. Descriptive Statistics. 2.1. Frequency Distributions and Their Graphs. 2.2. More Graphs and Displays. 2.3. Measures of Central Tendency. 2.4. Measures of Variation. 2.5. Measures of Position. Part Two. Probability & Probability Distributions. 3. Probability. 3.1. Basic Concepts of Probability and Counting. 3.2. Conditional Probability and the Multiplication Rule. 3.3. The Addition Rule. 3.4. Additional Topics in Probability and Counting. 4. Discrete Probability Distributions. 4.1. Probability Distributions. 4.2. Binomial Distributions. 4.3. More Discrete Probability Distributions. 5. Normal Probability Distributions. 5.1. Introduction to Normal Distributions and the Standard Normal Distribution. 5.2. Normal Distributions: Finding Probabilities. 5.3. Normal Distributions: Finding Values. 5.4. Sampling Distributions and the ...
A really good clinician not only embraces Bayes Theorem, they live and die by Bayes Theorem. Any veteran PA or NP makes decisions based on Bayes Theorem.
Methods for linking real-world healthcare data often use a latent class model, where the latent, or unknown, class is the true match status of candidate record-pairs. This commonly used model assumes that agreement patterns among multiple fields within a latent class are independent. When this assumption is violated, various approaches, including the most commonly proposed loglinear models, have been suggested to account for conditional dependence. We present a step-by-step guide to identify important dependencies between fields through a correlation residual plot and demonstrate how they can be incorporated into loglinear models for record linkage. This method is applied to healthcare data from the patient registry for a large county health department. Our method could be readily implemented using standard software (with code supplied) to produce an overall better model fit as measured by BIC and deviance. Finding the most parsimonious model is known to reduce bias in parameter estimates. This novel
TY - JOUR. T1 - Evaluation of the usefulness of a D dimer test in combination with clinical pretest probability score in the prediction and exclusion of Venous Thromboembolism by medical residents. AU - Owaidah, Tarek. AU - AlGhasham, Nahlah. AU - AlGhamdi, Saad. AU - AlKhafaji, Dania. AU - ALAmro, Bandar. AU - Zeitouni, Mohamed. AU - Skaff, Fawaz. AU - AlZahrani, Hazzaa. AU - AlSayed, Adher. AU - Elkum, Naser. AU - Moawad, Mahmoud. AU - Nasmi, Ahmed. AU - Hawari, Mohannad. AU - Maghrabi, Khalid. PY - 2014. Y1 - 2014. N2 - Introduction: Venous thromboembolism (VTE) requires urgent diagnosis and treatment to avoid related complications. Clinical presentations of VTE are nonspecific and require definitive confirmation by imaging techniques. A clinical pretest probability (PTP) score system helps predict VTE and reduces the need for costly imaging studies. D-dimer (DD) assay has been used to screen patients for VTE and has shown to be specific for VTE. The combined use of PTP and DD assay may ...
It may not look like much, but Bayes theorem is ridiculously powerful. It is used in medical diagnostics, self-driving cars, identifying email spam, decoding DNA, language translation, facial recognition, finding planes lost at the bottom of the sea, machine learning, risk analysis, image enhancement, analyzing Who wrote the Federalist Papers, Nate Silvers FiveThirtyEight.com, astrophysics, archaeology and psychometrics (among other things).[5][6][7] If you are into science, this equation should give you some serious tumescence. There are some great videos on the web about how to do conditional probability so check them out if you are wishing to know more about it. External links are provided on the bottom of this page. Let us now use breast cancer screening as a example of how Bayes theorem is used in real life. Please keep in mind that this is just an illustration. If you have concerns about your health, then you should consult with an oncologist. Let us say that a person is a 40-year-old ...
Bayes Theorem stated is, the conditional probability of A given B is the conditional probability of B given A scaled by the relative probability of A compared to B. I find it easier to understand through a practical explanation. Lets say you are having a medical test performed at the recommendation of your doctor, who recommends … Continue reading A Brief Introduction to Bayes Theorem. ...
Bayes Theorem stated is, the conditional probability of A given B is the conditional probability of B given A scaled by the relative probability of A compared to B. I find it easier to understand through a practical explanation. Lets say you are having a medical test performed at the recommendation of your doctor, who recommends … Continue reading A Brief Introduction to Bayes Theorem. ...
As it so happens, I am finishing a PhD in the theory of probability. I may not be recognized as a world-class expert on the subject, but I may be able to contribute some useful thoughts here.. Anyway, I agree with you that the Bayesian approach cannot produce precise numerical values for the probability of historical events. So were not going to get a definite probability of Jesus existence that way. I do think, however, that the Bayesian framework can still be useful in a more qualitative way.. The basic Bayesian idea is that we have some set of mutually exclusive hypotheses H1, H2, and so on. We assign some initial (prior) probability to each of those hypotheses. We then make some observation O. There will be some conditional probability P(O,H1), which is the probability of observing O given that H1 is true. Likewise for all the other hypotheses. These conditional probabilities are called the likelihoods. Bayes theorem then allows us to move to a final probability P(H1,O), which is the ...
This article offers a formal identification analysis of the problem in comparing coefficients from linear probability models between groups. We show that differences in coefficients from these models can result not only from genuine differences in effects, but also from differences in one or more of the following three components: outcome truncation, scale parameters and distributional shape of the predictor variable. These results point to limitations in using linear probability model coefficients for group comparisons. We also provide Monte Carlo simulations and real examples to illustrate these limitations, and we suggest a restricted approach to using linear probability model coefficients in group comparisons ...
The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoffs bound, Hoeffdings inequality,
Veritasium makes educational videos, mostly about science, and recently they recorded one offering an intuitive explanation of Bayes Theorem. They guide the viewer through Bayes thought process coming up with the theory, explain its workings, but also acknowledge some of the issues when applying Bayesian statistics in society. The thing we forget in Bayes Theorem is…
The probability mass function of a pair of discrete random variables is the function The conditional mass function of given is the function Thus the mass function lefthand plot computes probabilities of intersections while the conditional mass function righthand plot computes conditional probabilities For each value the slice through the conditional mass function at that value gives the distribu
I ran into a coin flip problem where flipping 4 coins has a 6/16 or 3/8 probability of landing 2 heads and 2 tails. I expected this value to be 1/2, because you have a 50% chance of getting heads or tails. Then that is only 6 of the possible 16 outcomes, instead of 8. Then I realized that the num...
Entering commands on touchscreens can be noisy, but existing interfaces commonly adopt deterministic principles for deciding targets and often result in errors. Building on prior research of using Bayes theorem to handle uncertainty in input, this paper formalized Bayes theorem as a generic guiding principle for deciding targets in command input (referred to as BayesianCommand), developed three models for estimating prior and likelihood probabilities, and carried out experiments to demonstrate the effectiveness of this formalization. More specifically, we applied BayesianCommand to improve the input accuracy of (1) point-and-click and (2) word-gesture command input. Our evaluation showed that applying BayesianCommand reduced errors compared to using deterministic principles (by over 26.9% for point-and-click and by 39.9% for word-gesture command input) or applying the principle partially (by over 28.0% and 24.5%).. ...
Conditional probability, Independence of events. tutorial of Probability Theory and Applications course by Prof Prabha Sharma of IIT Kanpur. You can download the course for FREE !
Federal Reserve rate hikes can send shockwaves through stock markets and put many people to sleep. But just because the nitty-gritty of the countrys fiscal policy isnt exciting to most does not mean were unaffected.. For one thing, the Feds seven rate hikes since Dec. 2015 have cost credit card users an extra $9.65 billion in interest to date. That figure will swell by at least $1.6 billion this year if the Fed raises its target rate on September 26, as expected. One more rate hike is expected from the Fed in the final quarter of 2018, too.. The rising cost of debt puts a lot of pressure on consumers. For example, it will take the average person in Magnolia, TX nearly 13 years to pay off his or her balance. With that in mind, WalletHub also conducted a nationally representative survey to gauge public sentiment. And while most people still have some homework to do, weve got no shortage of opinions.. Below, you can find everything you need to know about Federal Reserve interest rate ...
The Egyptian Journal of Chest Diseases and Tuberculosis, The Official Journal of Egyptian Society of Chest Diseases and Tuberculosis AND Arab Thoracic Association
Patient A: Female patient in ED, ,1 year old, fever with no definitive source on examination, pretest probability of UTI is 7%. Patient B: Male patient in ED, ,1 year old, circumcised, fever with no definitive source on examination, pretest probability of UTI is 0.5%. Patient C: Male patient in ED, ,1 year old, uncircumcised, fever with no definitive source on examination, pretest probability of UTI is 8%. Patient D: Female patient in ED, 2-6 years old, no fever but GU symptoms, pretest probability of UTI is 6.5%. Patient E: Female patient in ED, adolescent age range, no fever but urinary symptoms, pretest probability of UTI is 9% ...
This Conditional Probability: Game Show with Monty Interactive is suitable for 9th - 12th Grade. The car is behind door one - no wait, it is behind door three. An interactive allows learners to visualize the Monty Hall problem.
1. Random events, probability, probability space.. 2. Conditional probability, Bayes theorem, independent events.. 3. Random variable - definition, distribution function.. 4. Characteristics of random variables.. 5. Discrete random variable - examples and usage.. 6. Continuous random variable - examples and usage.. 7. Independence of random variables, sum of independent random variables.. 8. Transformation of random variables.. 9. Random vector, covariance and correlation.. 10. Central limit theorem.. 11. Random sampling and basic statistics.. 12. Point estimation, method of maximum likelihood and method of moments, confidence intervals.. 13. Confidence intervals.. 14. Hypotheses testing.. ...
As you have described it, there is not enough information to know how to conditional probability of the child from the parents. You have described that you have the marginal probabilities of each node; this tells you nothing about the relationship between nodes. For example, if you observed that 50% of people in a study take a drug (and the others take placebo), and then you later note that 20% of the people in the study had an adverse outcome, you do not have enough information to know how the probability of the child (adverse outcome) depends on the probability of the parent (taking the drug). You need to know the joint distribution of the parents and child to learn the conditional distribution. The joint distribution requires that you know the probability of the combination of all possible values for the parents and the children. From the joint distribution, you can use the definition of conditional probability to find the conditional distribution of the child on the parents.. ...
A law of probability that describes the proper way to incorporate new evidence into prior probabilities to form an updated probability estimate. Bayesian rationality takes its name from this theorem, as it is regarded as the foundation of consistent rational reasoning under uncertainty. A.k.a. Bayess Theorem or Bayess Rule. The theorem commonly takes the form: ...
MOTIVATION Mutagenicity is among the toxicological end points that pose the highest concern. The accelerated pace of drug discovery has heightened the need for efficient prediction methods. Currently, most available tools fall short of the desired degree of accuracy, and can only provide a binary classification. It is of significance to develop a discriminative and informative model for the mutagenicity prediction. RESULTS Here we developed a mutagenic probability prediction model addressing the problem, based on datasets covering a large chemical space. A novel molecular electrophilicity vector (MEV) is first devised to represent the structure profile of chemical compounds. An extended support vector machine (SVM) method is then used to derive the posterior probabilistic estimation of mutagenicity from the MEVs of the training set. The results show that our model gives a better performance than TOPKAT (http://www.accelrys.com) and other previously published methods. In addition, a confidence level
but this is not a continuous function, as only the numbers 1 to 6 are possible. In contrast, two people will not have the same height, or the same weight. Using a probability density function, it is possible to determine the probability for people between 180 centimetres (71 in) and 181 centimetres (71 in), or between 80 kilograms (176.4 lb) and 81 kilograms (178.6 lb), even though there are infinitely many values between these two bounds. ...
Were now going to review some of the basic concepts from probability. Well discuss expectations and variances, well discuss Bayes theorem, and well also review some of the commonly used distributions from probability theory. These include the binomial and Poisson distributions as well as the normal and log normal distributions. First of all, I just want to remind all of us whats a cumulative distribution function is. A CDF, a cumulative distribution function is f of x, were going to use f of x to denote the CDF and we define f of x to be equal to a probability that a random variable x is less than or equal to little x. Okay. We also, for discrete random variables, have whats called a probability mass function. Okay. And a probability mass function, which well denote with little p, it satisfies the following properties. P is greater than or equal to 0, and for all events, A, we have that the probability that x is in A, okay, is equal to the sum of p of x over all those outcomes x that ...
The shortest interval approach can be solved as an optimization problem, while the equally tailed approach is determined by using the distribution function. The equal density approach is proposed instead of the optimization problem for determining the shortest confidence interval. It is applied to multimodal probability density functions to determine the shortest confidence interval. Furthermore, the equal density and optimization approach for the shortest confidence interval and the equally tailed approach were applied to numerical examples and their results were compared. Nevertheless, the main subject of this study is the calculation of the shortest confidence intervals for any multimodal distribution. ...
Video created by Universidade da Califórnia, Santa Cruz for the course Bayesian Statistics: From Concept to Data Analysis. In this module, we review the basics of probability and Bayes theorem. In Lesson 1, we introduce the different paradigms ...
Downloadable! Implied probability density functions (PDFs) estimated from cross-sections of observed option prices are gaining increasing attention amongst academics and practitioners. To date, however, little attention has been paid to the robustness of these estimates or to the confidence that users can place in the summary statistics (for example the skewness or the 99th percentile) derived from fitted PDFs. This paper begins to address these questions by examining the absolute and relative robustness of two of the most common methods for estimating implied PDFs - the double-lognormal approximating function and the smoothed implied volatility smile methods. The changes resulting from randomly perturbing quoted prices by no more than a half tick provide a lower bound on the confidence intervals of the summary statistics derived from the estimated PDFs. Tests are conducted using options contracts tied to short sterling futures and the FTSE 100 index - both trading on the London International Financial
We describe an event tree scheme to quantitatively estimate both long- and short-term volcanic hazard. The procedure is based on a Bayesian approach that produces a probability estimation of any possible event in which we are interested and can make use of all available information including theoretical models, historical and geological data, and monitoring observations. The main steps in the procedure are (1) to estimate an a priori probability distribution based upon theoretical knowledge, (2) to modify that using past data, and (3) to modify it further using current monitoring data. The scheme allows epistemic and aleatoric uncertainties to be dealt with in a formal way, through estimation of probability distributions at each node of the event tree. We then describe an application of the method to the case of Mount Vesuvius. Although the primary intent of the example is to illustrate the methodology, one result of this application merits...
probability density function (pdf) over the entire area of the dartboard (and, perhaps, the wall surrounding it) must be equal to 1, since each dart must land somewhere.. The concept of the probability distribution and the random variables which they describe underlies the mathematical discipline of probability theory, and the science of statistics. There is spread or variability in almost any value that can be measured in a population (e.g. height of people, durability of a metal, etc.); almost all measurements are made with some ...

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Probability mass, Probability mass function, p.m.f., Discrete probability distribution function: for discrete random variables. ... A probability distribution of X is the pushforward measure X*P of X , which is a probability measure on (. X. ,. A. ). {\ ... Probability density, Probability density function, p.d.f., Continuous probability distribution function: most often reserved ... Continuous probability distribution[edit]. See also: Probability density function. A continuous probability distribution is a ...
Frequentist probability or frequentism is an interpretation of probability; it defines an events probability as the limit of ... subjective probability and frequency interpretations.. *Classical probability assigns probabilities based on physical idealized ... a b Keynes, John Maynard; A Treatise on Probability (1921), Chapter VIII "The Frequency Theory of Probability". ... Jerzy Neyman, First Course in Probability and Statistics, 1950. *Hans Reichenbach, The Theory of Probability, 1949 (German ...
... is the branch of mathematics concerned with analysis of random phenomena.[1] The central objects of ... Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in ... The mathematical theory of probability has its roots in attempts to analyze games of chance by Gerolamo Cardano in the ... Initially, probability theory mainly considered discrete events, and its methods were mainly combinatorial. Eventually, ...
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The total area under the curve is 1, so its a valid probability distribution. The area between x = 1 and x = 2 is 1/2, or 50 ... I know its the most controversal part , of MW and that there are several competing understandings of , probability in MW, but ... The fact that theres an infinite number of choices doesnt mean that those choices cant be normalized to a probability ... Physics is filled with probabilities over infinite domains. Anna --~--~---------~--~----~------------~-------~--~----~ You ...
The compound probability is equal to the probability of the first event multiplied by the probability of the second event. ... Compound probabilities are used by insurance underwriters to assess risks and assign premiums to various insurance products. ... The compound probability is equal to the probability of the first event multiplied by the probability of the second event. ... BREAKING DOWN Compound Probability. The most basic example of compound probability is flipping a coin twice. If the ...
... is a type of probability derived from an individuals personal judgment about whether a specific outcome ... What Is Subjective Probability? Subjective probability is a type of probability derived from an individuals personal judgment ... How Objective Probability Works. Objective probability is the probability that an event will occur based on an analysis in ... Subjective probability can be contrasted with objective probability, which is the computed probability that an event will occur ...
Understand how non-probability sampling can give you the results you need! ... Common non-probability sampling strategies. Here are some non-probability sampling designs that are used regularly, even if ... Probability sampling is favored by statisticians, but for people conducting surveys in the real world, non-probability sampling ... The biggest challenge of non-probability sampling is recreating the same kind of non-biased results that probability sampling ...
The probability formula of the law of radioactive decay is the unique probability law with the "no memory" property that the ... It is "improper" since the probability assigned to all the unit time intervals taken together is not one, as the probability ... This example is developed in Section 8.3 of "Probability Disassembled" and in "Induction without Probabilities.". The story ... Indeed many people seem to believe that probability theory provides the One True Logic of induction. Probability theory didnt ...
The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ... A union probability is denoted by P(X or Y), where X and Y are two events. P(X or Y) is the probability that X will occur or ... The probability of a person wearing glasses or having blond hair is an example of union probability. All people wearing glasses ... Probability. The probability of a certain event is a number expressing the likelihood that a specific event will occur, ...
... in which a casino or bookmaker evaluates the contestants in a competition and assesses the probability of victory: 2 to 1, 5 to ...
... is designed for the publication of workshops, seminars and conference proceedings on all aspects of ... Get the table of contents of every new volume published in Progress in Probability. ... probability theory and stochastic processes, as well as their connections with and applications to other areas such as ...
The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ... Asked in Probability. , Twilight New Moon What is the probability in book new moon. ?. ... Probability. The probability of a certain event is a number expressing the likelihood that a specific event will occur, ... Asked in Probability What is the probability of getting at least two tails. ?. ...
... the resultant probability is the product of the individual probabilities. If you want the probability of throwing a 7 with a ... Basic Probability The probability for a given event can be thought of as the ratio of the number of ways that event can happen ... Probability of throwing a "2" with a single die: 1/6 *Probability of throwing "2" twice in a row, "2" AND "2": 1/6 x 1/6=1/36 * ... For example, the probability of drawing five cards of any one suit is the sum of four equal probabilities, and four times as ...
... This is a free, online wikibook, so its content is continually being updated and refined. According to the authors ... You just viewed Probability. Please take a moment to rate this material. ... "This book is an introduction to the mathematical theory of probability." ...
This fact sheet addresses four common questions concerning the probability of causation ... This fact sheet addresses four common questions concerning the probability of causation (defined below). Q: What is probability ... Q: How will I know if I will be compensated? A: The probability of causation is expressed as a percentage between 0% and 100%. ... Q: How accurate is the calculation for probability of causation? A: The calculation is a high estimate of the likelihood or " ...
... determining probability of causation, for each claim for which NIOSH is required to complete a radiation dose reconstruction. ... Probability of Causation Final Rule. On May 2, 2002, the Department of Health and Human Services published its final rule on ... Public Comments on the Probability of Causation Rule. The final Rule on PC went into effect after the public the Advisory Board ... Guidelines for Determining the Probability of Causation-42 CFR 81 pdf icon[552 KB (12 pages)]. October 5, 2001 ...
... in probability and stochastic processes, with a particular focus on: ... ... The Probability and Its Applications series publishes research monographs, with the expository quality to make them useful and ... in probability and stochastic processes, with a particular focus on: -Foundations of probability including stochastic analysis ... The Probability and Its Applications series publishes research monographs, with the expository quality to make them useful and ...
... describes probability as the amount of evidence that accompanies uncertainty, a reasoning from conjecture. Probability theory ... David Hume, the renowned philosopher in his Treatise of Human Nature, describes probability as the amount of evidence that ... Probability theory is the branch of mathematics dealing with the study of uncertainty. ... Ghatak A. (2017) Probability and Distributions. In: Machine Learning with R. Springer, Singapore. * DOI https://doi.org/10.1007 ...
... as defined by the probability density function. Source for information on probability distribution: A Dictionary of Earth ... probability distribution In statistics, the relative frequency distribution of different events occurring, ... as defined by the probability density function. Probability distributions may be discrete as in the cases of the binomial and ... probability distribution A Dictionary of Earth Sciences © A Dictionary of Earth Sciences 1999, originally published by Oxford ...
The simplest probability model is the Gaussian, or normal, distribution, of which there are many examples in biology, medicine ... Source for information on Probability Model: Encyclopedia of Public Health dictionary. ... PROBABILITY MODEL A probability model, also known as a stochastic model, is a mathematical formulation that incorporates an ... PROBABILITY MODEL. A probability model, also known as a stochastic model, is a mathematical formulation that incorporates an ...
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Organization of the Mini-Workshop Perspectives in High-dimensional Probability and Convexity. (jointly with Joscha Prochno and ... Organization of the Spring School and Workshop on Polytopes: Geometry, Combinatorics and Probability. (jointly with Martina ... Talk of Christoph Thäle in the seminar on Probability Theory and Stochastic Analysis. Bonn, Germany. January 19, 2017 ... 12th International Vilnius Conference on Probability Theory and Mathematical Statistics + 2018 IMS Annual Meeting on ...
probability mass function, p such that. Continuous probability distribution. By one convention, a probability distribution is ... probability axioms are satisfied. That is, probability distributions are probability measures defined over a state space ... A probability distribution describes the values and probabilities that a random event can take place. The values must cover all ... Because a probability distribution Pr on the real line is determined by the probability of being in a half-open interval Pr(a, ...
Unique interpretation of probability theory, containing new and original work by the author • Applications of probability ... Probability Theory. The Logic of Science. E. T. Jaynes. Edited by G. Larry Bretthorst ... The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels ... This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results ...
... branch of mathematics concerning probability (en); branch of mathematics concerning probability (en); matematiikan osa-alue (fi ... Các tập tin trong thể loại "Probability theory". 133 tập tin sau nằm trong thể loại này, trong tổng số 133 tập tin. ... Continuous p-box showing interval probability interval(0.4, 0.36) that x is 2.5 or less.png 960×720; 11 kB. ... teoría de la probabilidad (es); Líkindafræði (is); Teori kebarangkalian (ms); Уæвæны теори (os); probability theory (en-gb); ...
The probability of an event A is written P(A). The principle of addition of probabilities is that, if A1, A2,…, An are events ... probability theory: The principle of additivity: The impossible event-i.e., the event containing no outcomes-is denoted by Ø. ... The probability of an event A is written P(A). The principle of addition of probabilities is that, if A1, A2,…, An are events ... In probability theory: The principle of additivity. The impossible event-i.e., the event containing no outcomes-is denoted by Ø ...
SVMModel::predict_probability. (PECL svm ,= 0.1.4). SVMModel::predict_probability - Return class probabilities for previous ... probabilities. The supplied value will be filled with the probabilities. This will be either null, in the case of a model ... public SVMModel::predict_probability ( array $data. ) : float. This function accepts an array of data and attempts to predict ... Additionally, however, this function returns an array of probabilities, one per class in the model, which represent the ...
While the selection probabilities in examples 1 and 2 are known, the response or non-censoring probabilities in examples 3 and ... Inverse probability weighting can also be used when individuals vary in their probability of having missing information. Two ... Inverse probability weighting can be used with weights estimated from a logistic regression model for predicting non-response ... Seaman SR, White IR.. Review of inverse probability weighting for dealing with missing data. Stat Methods Med Res 2013;22: 278- ...
... a random sample of 100 grapefruits from the same orchard and the mean diameter is calculated what is the probability that the ... Probability models Your stockbroker has a 65 percent probability of success in picking stocks that appreciate? ... Percent and probability? if grapefruits in an orchard are normally distributed with a mean of 5.93 in and sd of 0.59i what % ... So the probability of grapefruits in an orchard larger than 5.88 is = P (x , 5.88) = P (z , -0.085) = 0.533869305 = 53.39 % ...
  • This article is about probability distributions. (wikipedia.org)
  • Probability distributions are generally divided into two classes. (wikipedia.org)
  • Important and commonly encountered univariate probability distributions include the binomial distribution , the hypergeometric distribution , and the normal distribution . (wikipedia.org)
  • To define probability distributions for the simplest cases, it is necessary to distinguish between discrete and continuous random variables . (wikipedia.org)
  • Ghatak A. (2017) Probability and Distributions. (springer.com)
  • Probability distributions may be discrete as in the cases of the binomial and Poisson distributions , or continuous as in the case of the normal distribution . (encyclopedia.com)
  • numbers are often inadequate for describing a quantity, while probability distributions are often more appropriate models. (mcgill.ca)
  • To download the free app Probability-Distributions by Matthew Bognar, get iTunes now. (apple.com)
  • Theory of probability distributions ‎ (1 t.l. (wikimedia.org)
  • This book offers an introduction to concepts of probability theory, probability distributions relevant in the applied sciences, as well as basics of sampling distributions, estimation and hypothesis testing. (eurekalert.org)
  • Probability - Perl extension for calculating dice probabilities and distributions. (cpan.org)
  • Probability calculates probabilities and distributions for complex dice expressions. (cpan.org)
  • A wide-range of topics are covered that include the concepts of probability and conditional probability, univariate discrete distributions, univariate continuous distributions, along with a detailed presentation of the most important probability distributions used in practice, with their main properties and applications. (wiley-vch.de)
  • For most of the classical distributions, base R provides probability distribution functions (p), density functions (d), quantile functions (q), and random number generation (r). (r-project.org)
  • Thesaurus of univariate discrete probability distributions by G. Wimmer and G. Altmann. (r-project.org)
  • This help page describes the probability distributions provided in the Statistics package, how to construct random variables using these distributions and the functions that are typically used in conjunction with these distributions. (maplesoft.com)
  • Discrete distributions have nonzero probability only at discrete points. (maplesoft.com)
  • Discrete distributions are defined by their probability function rather than by their probability density function in order to avoid singularities. (maplesoft.com)
  • More complex experiments, such as those involving stochastic processes defined in continuous time , may demand the use of more general probability measures . (wikipedia.org)
  • Progress in Probability is designed for the publication of workshops, seminars and conference proceedings on all aspects of probability theory and stochastic processes, as well as their connections with and applications to other areas such as mathematical statistics and statistical physics. (springer.com)
  • Theory of Probability and its Applications (TVP) is a translation of the Russian journal Teoriya Veroyatnostei i ee Primeneniya , which contains papers on the theory and application of probability, statistics, and stochastic processes. (siam.org)
  • Conditional probability ‎ (17 t.t. (wikimedia.org)
  • The conditional probability of word w4 given the sequence w1,w2,w3. (ibm.com)
  • It then evolves toward the rigorous study of discrete and continuous probability spaces, independence, conditional probability, expectation, and variance. (amherst.edu)
  • H) is the jointly probability to hiring a black worker conditional on being a H worker. (stata.com)
  • In probability theory and statistics , a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment . (wikipedia.org)
  • A probability distribution is specified in terms of an underlying sample space , which is the set of all possible outcomes of the random phenomenon being observed. (wikipedia.org)
  • A discrete probability distribution (applicable to the scenarios where the set of possible outcomes is discrete , such as a coin toss or a roll of dice) can be encoded by a discrete list of the probabilities of the outcomes, known as a probability mass function . (wikipedia.org)
  • On the other hand, a continuous probability distribution (applicable to the scenarios where the set of possible outcomes can take on values in a continuous range (e.g. real numbers), such as the temperature on a given day) is typically described by probability density functions (with the probability of any individual outcome actually being 0). (wikipedia.org)
  • countable number of discrete outcomes with positive probabilities. (mcgill.ca)
  • If the process under study can be repeated or simulated many times, we can determine the empirical probability by keeping track of the outcomes in our (large number of) trials. (calvin.edu)
  • When dealing with probability, the outcomes of a process are the possible results. (sparknotes.com)
  • The probability of an event, like rolling an even number, is the number of outcomes that constitute the event divided by the total number of possible outcomes. (sparknotes.com)
  • Remember that the sum of the probabilities of all possible outcomes is 1. (bbc.co.uk)
  • When dealing with experiments that are random and well-defined in a purely theoretical setting (like tossing a fair coin), probabilities can be numerically described by the number of desired outcomes, divided by the total number of all outcomes. (wikipedia.org)
  • This interpretation considers probability to be the relative frequency "in the long run" of outcomes. (wikipedia.org)
  • Introduction to Probability offers an authoritative text that presents the main ideas and concepts, as well as the theoretical background, models, and applications of probability. (wiley-vch.de)
  • Written for students majoring in statistics, engineering, operations research, computer science, physics, and mathematics, Introduction to Probability: Models and Applications is an accessible text that explores the basic concepts of probability and includes detailed information on models and applications. (wiley-vch.de)
  • Now if you never studied probability and would like to learn the basics, of if you don't remember it anymore but would like a refresher, check a post I wrote on my programming blog titled Introduction to Probability. (dailyblogtips.com)
  • probability distribution In statistics, the relative frequency distribution of different events occurring, as defined by the probability density function . (encyclopedia.com)
  • probability density function (pdf) over the entire area of the dartboard (and, perhaps, the wall surrounding it) must be equal to 1, since each dart must land somewhere. (mcgill.ca)
  • Probability theory is the branch of mathematics concerned with analysis of random phenomena. (princeton.edu)
  • Offered as STAT 360 and MATH 360) This course explores the nature of probability and its use in modeling real world phenomena. (amherst.edu)
  • The epistemological value of probability theory is based on the fact that chance phenomena, considered collectively and on a grand scale, create non-random regularity. (wikiquote.org)
  • Probability focuses fundamentally on the modelling of random phenomena, i.e. those subject to uncertainty. (impa.br)
  • Though probabilities are calculated as fractions, they can be converted to decimals or percents-- the Fractions SparkNote in Pre-Algebra explains how to convert fractions to decimals and the SparkNote on Percents describes how to convert them to percents. (sparknotes.com)
  • With this exercise, your child will practice using fractions to express probability. (education.com)
  • Then they can build on their math skills and fractions prowess with probability games involving darts, coins, and jelly beans that are as entertaining as they are educational. (education.com)
  • Kids will practice with fractions and degrees in this probability worksheet. (education.com)
  • Probabilities can be written as fractions, decimals or percentages. (bbc.co.uk)
  • #Trigonometry # Probability #Area #BasicOperations #QuadraticFormula #Percentages , #Fractions , #Decimals #Graphicalinterpretation #Formula Speak to us. (twitter.com)
  • The probability of an event is based on the likelihood of that event occurring. (investopedia.com)
  • In most forms of probability, quantitative information is gathered and interpreted to help determine this likelihood through a mathematical mechanism, normally relating to the mathematical field of statistics. (investopedia.com)
  • Default probability is the likelihood over a specified period, usually one year, that a borrower will not be able to make scheduled repayments. (investopedia.com)
  • The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. (answers.com)
  • A: The calculation is a high estimate of the likelihood or "probability" that the cancer covered by your claim might have been related to the amount of radiation dose in your dose reconstruction. (cdc.gov)
  • DOL will use the energy employee's personal characteristics, employment information, medical information, and dose reconstruction results to determine the Probability of Causation (PC)-that is, the likelihood that the worker's cancer was caused by exposure to radiation during employment. (cdc.gov)
  • Probability is a measure of the likelihood of some event happening. (calvin.edu)
  • Becuase people often have a poor sense of the likelihood of an event, personal probabilities often do not follow these rules. (calvin.edu)
  • This series of maps shows the probability (that is, the likelihood) that snowfall will equal or exceed specific amounts during the time period shown on the graphic. (weather.gov)
  • Probability is a measure of the likelihood that an event will happen. (sparknotes.com)
  • Probability, which is the value assigned to the likelihood of an event occurring, can take on any numerical value between and including 0 and 1. (ti.com)
  • The product of the prior and the likelihood, when normalized, results in a posterior probability distribution that incorporates all the information known to date. (wikipedia.org)
  • Receive email alerts on new books, offers and news in Statistics & Probability 2017 Catalogue. (cambridge.org)
  • Statistical probability" redirects here. (wikipedia.org)
  • For the episode of Star Trek: Deep Space Nine, see Statistical Probabilities . (wikipedia.org)
  • Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics . (princeton.edu)
  • A probability distribution is a statistical function that describes possible values and likelihoods that a random variable can take within a given range. (investopedia.com)
  • In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. (cambridge.org)
  • Probabilists from the Department of Statistics also have strong links and take part in many research activities with the Department of Mathematics, particularly those organised by the probability and statistical mechanics groups. (warwick.ac.uk)
  • A probability cone uses historical option data and a proprietary statistical formula in order to the graph the potential future range for stock prices. (scottrade.com)
  • This allows you to combine the knowledge of an expected price range based on statistical data with time series data to estimate the probability that your option trade has the potential to be in the money by expiration and theoretically its value. (scottrade.com)
  • In a sense, this differs much from the modern meaning of probability, which in contrast is a measure of the weight of empirical evidence, and is arrived at from inductive reasoning and statistical inference. (wikipedia.org)
  • For instance, if the random variable X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 for X = heads , and 0.5 for X = tails (assuming the coin is fair). (wikipedia.org)
  • The most basic example of compound probability is flipping a coin twice. (investopedia.com)
  • The percentage chance of a flipped coin landing on heads or tails can be interpreted as a probability, expressed as a 50% chance that it will land heads up, and a 50% chance it will land tails up. (investopedia.com)
  • Even knowing that the new prediction is mathematically inaccurate, the individual's personal experience of the previous 10 coin flips has created a situation in which he chooses to use subjective probability. (investopedia.com)
  • There is probability of a half that a coin tossed fairly will come up heads. (pitt.edu)
  • Our degrees of belief ought to conform to the probability calculus just because the physical chances of the coin tosses conform to that same calculus. (pitt.edu)
  • these two values and two probabilities make up the probability distribution of the single coin flipping event. (mcgill.ca)
  • Delve into the inner-workings of coin toss probability with this activity. (education.com)
  • By John Timmer, Ars Technica The World Science Festival's panel on Probability and Risk started out in an unusual manner: MIT's Josh Tennenbaum strode onto a stage and flipped a coin five times, claiming he was psychically broadcasting each result to the audience. (wired.com)
  • The concept of probability is one of the foundations of general statistics . (gsu.edu)
  • Kids will learn about the important concept of probability by counting gummy bears in a bag. (education.com)
  • The Probability Program supports research on the theory and applications of probability. (nsf.gov)
  • New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. (cambridge.org)
  • With a focus on models and tangible applications of probability from physics, computer science, and other related disciplines, this book successfully guides readers through fundamental coverage for enhanced understanding of the problems. (wiley-vch.de)
  • Empirical probability uses the number of occurrences of an outcome within a sample set as a basis for determining the probability of that outcome. (investopedia.com)
  • Empirical probabilities will also follow these rules (for a given set of trials). (calvin.edu)
  • The probabilty then is given by (number of interest)/(total number), just as in the case for empirical probability. (calvin.edu)
  • There are two explicit complementary goals: to explore probability theory and its use in applied settings, and to learn parallel analytic and empirical problem solving skills. (amherst.edu)
  • Asymptotic methods in probability and statistics, short and long range dependence, empirical processes of dependent data, U-statistics, nonparametric statistics, vector-valued processes, change-point analysis for time series. (ruhr-uni-bochum.de)
  • In this lesson, students use simulations to explore the relationship between the theoretical probability and the empirical probability. (ti.com)
  • Sometimes we can make mathemitical assumptions about a situation and use Four Basic Properties of Probability to determine the theoretical probability of an event. (calvin.edu)
  • The accuracy of a theoretical probability depends on the validity of the mathematical assumptions made. (calvin.edu)
  • How to find theoretical probabilities of normal distribution in a data frame in R? (stackoverflow.com)
  • They understand how to represent the theoretical probability for an event and can interpret the long-run relative frequency of an event. (ti.com)
  • Students should notice that the more repetitions of an experiment leads to an relative frequency that is closer to the theoretical probability. (ti.com)
  • Subjective probability is a type of probability derived from an individual's personal judgment or own experience about whether a specific outcome is likely to occur. (investopedia.com)
  • Subjective probability can be contrasted with objective probability , which is the computed probability that an event will occur based on an analysis in which each measure is based on a recorded observation or a long history of collected data. (investopedia.com)
  • Objective probability is the probability that an event will occur based on an analysis in which each measurement is based on a recorded observation. (investopedia.com)
  • If you want the probabability that any one of a number of disjoint events will occur, the probabilities of the single events can be added. (gsu.edu)
  • In addition, we will use the term personal probability for a statement of someone's degree of belief that an event will occur. (calvin.edu)
  • The higher the probability of an event, the more certain that the event will occur. (wikiquote.org)
  • Due to probability, sometimes an event is more likely to occur than we believe it to. (scientificamerican.com)
  • Students recognize that probability measures the chance that an event will occur. (ti.com)
  • The higher the probability, the more likely the event is to occur. (ti.com)
  • the probability that an event will occur under the condition that another event occurs first: equal to the probability that both will occur divided by the probability that the first will occur. (dictionary.com)
  • Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. (wikipedia.org)
  • He is a Fellow of the Institute of Mathematical Statistics and has written a graduate level text on probability theory. (google.com)
  • The journal accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. (siam.org)
  • Herold Dehling has been chair of the Scientic Programme Committees of several major conferences, e.g. the 2006 European Meeting of Statisticians, the 2012 German Probability and Statistics Days, and the 2013 German-Polish Joint Conference on Probability and Mathematical Statistics. (ruhr-uni-bochum.de)
  • Dealing with basic probability as a discrete counting process is satisfactory if you have reasonably small numbers, like throwing dice or picking cards. (gsu.edu)
  • The Probability Aquarium is a Java applet that presents basic probability rules in the context of interactive questions based on selecting fish at random from an aquarium. (maa.org)
  • Practice calculating basic probability with this worksheet. (education.com)
  • The objective probability--the chances--are a half. (pitt.edu)
  • The most popular version of objective probability is frequentist probability, which claims that the probability of a random event denotes the relative frequency of occurrence of an experiment's outcome when the experiment is repeated indefinitely. (wikipedia.org)
  • Suppose you draw five cards from a standard deck of 52 playing cards, and you want to calculate the probability that all five cards are hearts. (gsu.edu)
  • When you calculate the probability by direct counting processes like those discussed above, then the probabilities are always normalized. (gsu.edu)
  • Calculate the mathematical probability of getting a sum higher than 18 for each combination of dice when rolling them 100 times. (scientificamerican.com)
  • This Web site can teach you how to calculate probability: Probability Central from Oracle ThinkQuest. (scientificamerican.com)
  • Bowl a strike as you calculate the probability of knocking down pins! (education.com)
  • These numerical weights are called probability amplitudes, and this relationship used to calculate probabilities from given pure quantum states (such as wave functions) is called the Born rule. (wikipedia.org)
  • For instance, when you use Google search or Facebook you are using it (i.e., there are algorithms in those services that rely on probability theory). (dailyblogtips.com)
  • But for any given word sequence, it should be possible to compute the probability of the next word. (ibm.com)
  • If we want to compute the probability of 'Sam' occurring next, how do we do this? (ibm.com)
  • The desire of the experts to publish and gain credit in the eyes of their peers has distorted the development of probability theory from the needs of the average user. (wikiquote.org)
  • What Is Subjective Probability? (investopedia.com)
  • Subjective probabilities differ from person to person and contain a high degree of personal bias. (investopedia.com)
  • An example of subjective probability is a 'gut instinct' when making a trade. (investopedia.com)
  • Subjective probability, on the other hand, is highly flexible, even in terms of one individual's belief. (investopedia.com)
  • Subjective probability can be affected by a variety of personal beliefs held by an individual. (investopedia.com)
  • An example of subjective probability is asking New York Yankees fans, before the baseball season starts, about the chances of New York winning the World Series . (investopedia.com)
  • If there are objective chances to be had, your subjective probabilities should match them. (pitt.edu)
  • Some maintain that there exist two types of probability, as above, others, that only the subjective exists, because regardless of what is supposed to take place, we cannot have full knowledge of it. (wikiquote.org)
  • Subjective Probability - The Real Thing Any thoughts on whether they are good for beginners? (twitter.com)
  • Subjectivists assign numbers per subjective probability, that is, as a degree of belief. (wikipedia.org)
  • The degree of belief has been interpreted as "the price at which you would buy or sell a bet that pays 1 unit of utility if E, 0 if not E." The most popular version of subjective probability is Bayesian probability, which includes expert knowledge as well as experimental data to produce probabilities. (wikipedia.org)
  • The expert knowledge is represented by some (subjective) prior probability distribution. (wikipedia.org)
  • The compound probability is equal to the probability of the first event multiplied by the probability of the second event. (investopedia.com)
  • it defines an event's probability as the limit of its relative frequency in a large number of trials. (wikipedia.org)
  • The relative frequency of occurrence of an event, observed in a number of repetitions of the experiment, is a measure of the probability of that event. (wikipedia.org)
  • Mathematical probability is the measure of the relative frequency of an event occurring. (calvin.edu)
  • In the frequentist interpretation, probabilities are discussed only when dealing with well-defined random experiments (or random samples). (wikipedia.org)
  • This is the core conception of probability in the frequentist interpretation. (wikipedia.org)
  • Particularly when the frequency interpretation of probability is mistakenly assumed to be the only possible basis for frequentist inference . (wikipedia.org)
  • Posterior probability is the revised probability of an event occurring after taking into consideration new information. (investopedia.com)
  • A probability distribution whose sample space is one-dimensional (for example real numbers, list of labels, ordered labels or binary) is called univariate , while a distribution whose sample space is a vector space of dimension 2 or more is called multivariate . (wikipedia.org)
  • Perhaps the most widely used distribution function in classical physics is the Boltzmann distribution function, which describes the probability of finding particles with an amount of energy E at a given temperature T. (gsu.edu)
  • David Hume, the renowned philosopher in his Treatise of Human Nature , describes probability as the amount of evidence that accompanies uncertainty, a reasoning from conjecture. (springer.com)
  • continuous distribution describes events over a continuous range, where the probability of a specific outcome is zero. (mcgill.ca)
  • A smooth function that describes the probability of landing anywhere on the dartboard is the probability distribution of the dart throwing event. (mcgill.ca)
  • The normal distribution is a commonly encountered continuous probability distribution. (wikipedia.org)
  • Probability sampling is favored by statisticians, but for people conducting surveys in the real world, non-probability sampling is more practical. (surveymonkey.com)
  • books.google.com - Probability for Statisticians is intended as a text for a one year graduate course aimed especially at students in statistics. (google.com)
  • Besides anything that is impossible, as noted above, the simultaneous occurrence of two mutually exclusive events has a probability of zero: It is raining and it is not raining, it is on and it is off, etc. (answers.com)
  • Associates a particulare probability of occurrence with each outcome in the sample space. (answers.com)
  • The standard rules of probability can be interpreted as uniquely valid principles in logic. (cambridge.org)
  • The first part of the book systematically presents concepts and results from analysis before embarking on the study of probability theory. (oreilly.com)
  • The scientific study of probability is a modern development of mathematics. (wikipedia.org)
  • Whereas games of chance provided the impetus for the mathematical study of probability, fundamental issues are still obscured by the superstitions of gamblers. (wikipedia.org)
  • In other words the probability amplitudes are zero for all the other eigenstates, and remain zero for the future measurements. (wikipedia.org)
  • In other words, the probability amplitudes for the second measurement of Q depend on whether it comes before or after a measurement of R, and the two observables do not commute. (wikipedia.org)
  • Which answer you incline towards reveals where you stand in a 250-year-old, sometimes strangely vicious debate on the nature of probability and statistics. (newscientist.com)
  • However, when it comes to practical application, there are two major competing categories of probability interpretations, whose adherents hold different views about the fundamental nature of probability: Objectivists assign numbers to describe some objective or physical state of affairs. (wikipedia.org)
  • MIAMI (AP) -- The National Hurricane Center hopes to discourage residents from relying too much on that skinny black line in forecasts by offering a new map that shows the probability of an area being hit. (redorbit.com)
  • This introductory text is the product of his extensive teaching experience and is geared toward readers who wish to learn the basics of probability theory, as well as those who wish to attain a thorough knowledge in the field. (doverpublications.com)
  • Even if you are not working in any of those fields I think you should know at least the basics of probability, as it can be useful in your everyday life. (dailyblogtips.com)
  • # Probability Of Trade Going Wrong Is #Inversely Proportional To #TimeFrame Selected For Analysis Lower The TimeFrame, Higher The Probability Of Trade Going Wrong! (twitter.com)
  • A number of problems situated right at the boundary between analysis and probability theory have recently been at the centre of intense attention. (warwick.ac.uk)
  • Q: What information is used to determine the probability of causation? (cdc.gov)
  • A: Specific information about the energy employee is used to determine the probability of causation. (cdc.gov)
  • For application of probability to physical processes, the use of the distribution function is a very useful strategy. (gsu.edu)
  • What do statistics and probability reveal about the natural world? (edrants.com)
  • This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. (cambridge.org)
  • There are reasons for the slow development of the mathematics of probability. (wikipedia.org)
  • Probability theory is the branch of mathematics dealing with the study of uncertainty. (springer.com)
  • fno-guess-branch-probability switch. (gnu.org)
  • Probability theory is a relatively new mathematics branch. (dailyblogtips.com)
  • The probability mass function (pmf) p ( S ) specifies the probability distribution for the sum S of counts from two dice . (wikipedia.org)
  • assigning a probability to each possible outcome: for example, when throwing a fair dice , each of the six values 1 to 6 has the probability 1/6. (wikipedia.org)
  • In the classical interpretation, probability was defined in terms of the principle of indifference , based on the natural symmetry of a problem, so, e.g. the probabilities of dice games arise from the natural symmetric 6-sidedness of the cube. (wikipedia.org)
  • In the probability of a throw of a pair of dice , bet on the number 7 since it is the most probable. (gsu.edu)
  • Rolling dice is a great way to investigate probability. (scientificamerican.com)
  • Probability can be as easy as rolling dice! (education.com)
  • The simplest probability model is the Gaussian, or normal, distribution, of which there are many examples in biology, medicine, and public health . (encyclopedia.com)
  • Get some practice with probability! (education.com)
  • Spring into spring with some probability practice. (education.com)
  • Practice probability with the days of the week! (education.com)
  • This math worksheet offers students hands-on practice in calculating probability through simple, familiar scenarios. (education.com)
  • Here's a great opportunity for your child to practice probability! (education.com)
  • Practice probability by exploring the various odds that can be found in a standard deck of playing cards. (education.com)
  • Give your child some practice with probability! (education.com)
  • From July 2014 series continued as 'Probability Theory and Stochastic Modelling' PTSM (ISSN 2199-3130). (springer.com)
  • Experiment (probability theory) ‎ (7 t.l. (wikimedia.org)
  • For each of eight different questions increasing in complexity, the student performs sampling with or without replacement and then answers a probability question based on this experiment. (maa.org)
  • A modification of this is propensity probability, which interprets probability as the tendency of some experiment to yield a certain outcome, even if it is performed only once. (wikipedia.org)
  • Physics is filled with probabilities over infinite domains. (mail-archive.com)
  • The research center in Geometry, Physics and Probability (GPP) regroups researchers active in various areas of mathematics and mathematical physics which do not belong to the traditional subdomains of pure mathematics. (uclouvain.be)
  • These areas are related to complex analysis, mathematical physics and probability. (uclouvain.be)
  • Quota sampling ensures that you get at least some respondents from all the subpopulations you're interested in, even though this still isn't a true probability sample. (surveymonkey.com)
  • If done well, non-probability sampling can give you the same (or better) high-quality data you would expect from a true probability sample. (surveymonkey.com)

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