###### Probability Theory

###### Probability Learning

###### Models, Statistical

###### Bayes Theorem

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.

###### Algorithms

###### Computer Simulation

###### Markov Chains

###### Models, Genetic

###### Monte Carlo Method

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)

###### Models, Biological

###### Models, Theoretical

###### Stochastic Processes

###### Likelihood Functions

###### Data Interpretation, Statistical

###### Ion Channel Gating

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.

###### Predictive Value of Tests

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.

###### Decision Theory

###### Sensitivity and Specificity

###### Risk Factors

###### Reproducibility of Results

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.

###### Decision Support Techniques

###### Treatment Outcome

###### Patch-Clamp Techniques

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.

###### Logistic Models

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.

###### Retrospective Studies

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.

###### Nomograms

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.

###### Prospective Studies

###### Membrane Potentials

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).

###### Statistical Distributions

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.

###### Survival Analysis

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.

###### Prognosis

###### Risk Assessment

###### Cost-Benefit Analysis

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 Factors

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.

###### Choice Behavior

###### ROC Curve

###### Follow-Up Studies

###### Uncertainty

###### Electrophysiology

###### Cohort Studies

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.

###### Software

###### Synaptic Transmission

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.

###### Quality-Adjusted Life Years

###### Decision Trees

###### Synapses

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.

###### Regression Analysis

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.

###### Models, Neurological

###### Decision Making

###### Multivariate Analysis

###### Mutation

###### Computational Biology

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.

###### Mathematics

###### Excitatory Postsynaptic Potentials

###### Calcium

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.

###### Columbidae

###### Action Potentials

###### Population Dynamics

###### Prevalence

###### Potassium Channels

###### Statistics as Topic

###### Survival Rate

###### Normal Distribution

###### Genetics, Population

###### Models, Economic

###### Neurotransmitter Agents

###### Risk

###### Models, Chemical

###### Sample Size

###### Neurons

###### Genotype

###### Analysis of Variance

###### Sampling Studies

###### Alleles

###### Ion Channels

###### Synaptic Vesicles

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.

###### Incidence

###### Ventilation-Perfusion Ratio

###### Presynaptic Terminals

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.

###### Pregnancy

###### Entropy

###### Proportional Hazards Models

###### Bias (Epidemiology)

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.

###### Life Tables

###### Poisson Distribution

###### Biometry

###### Sex Factors

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.

###### Reward

###### Pattern Recognition, Automated

###### Biological Evolution

###### Confidence Intervals

###### Biostatistics

###### Databases, Factual

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.

###### False Positive Reactions

###### Selection, Genetic

###### Genetic Markers

###### Reinforcement Schedule

###### Disease-Free Survival

###### Severity of Illness Index

###### Dose-Response Relationship, Drug

###### Odds Ratio

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.

###### Gene Frequency

###### Epithelial Sodium Channels

###### Research Design

###### Evolution, Molecular

###### Molecular Sequence Data

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.

###### Cross-Sectional Studies

###### Kaplan-Meier Estimate

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)

###### Calcium Channels

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.

###### Health Surveys

###### Forecasting

###### Photic Stimulation

###### Longitudinal Studies

###### Linear Models

###### Cluster Analysis

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.

###### Disease Progression

###### Evoked Potentials

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.

###### Artificial Intelligence

###### Pedigree

###### Questionnaires

###### Ecosystem

###### Models, Psychological

###### Socioeconomic Factors

###### Sequence Analysis, Protein

###### Epidemiologic Methods

###### Neuronal Plasticity

###### Magnetic Resonance Imaging

###### Geography

###### Proteins

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.

###### Sequence Alignment

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.

###### Genetic Linkage

###### Image Processing, Computer-Assisted

###### Mathematical Computing

###### Demography

###### Bone Marrow Transplantation

###### Actuarial Analysis

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.

###### Nonlinear Dynamics

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.

###### Life Expectancy

###### Chromosome Mapping

###### Sodium Channels

###### Fibrin Fibrinogen Degradation Products

###### HIV Infections

###### Neural Networks (Computer)

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.

###### Sequence Analysis, DNA

###### Health Care Costs

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.

###### Game Theory

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.

###### Combined Modality Therapy

###### Statistics, Nonparametric

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)

###### Neoplasm Staging

###### Information Theory

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.

###### Data Collection

###### Transplantation, Homologous

###### Remission Induction

###### Neoplasms

###### Randomized Controlled Trials as Topic

###### Diagnosis, Computer-Assisted

###### Hippocampus

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, Molecular

###### Fertility

###### Phenotype

###### Base Sequence

###### Area Under Curve

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)

###### Diagnosis

###### Oocytes

###### Large-Conductance Calcium-Activated Potassium Channels

###### Breeding

###### Electroencephalography

###### Age Distribution

###### Heterozygote

###### Spain

###### Registries

###### Mass Screening

###### Neoplasm Recurrence, Local

###### Case-Control Studies

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.

###### Ryanodine Receptor Calcium Release Channel

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.

###### Graft vs Host Disease

###### Potassium Channels, Calcium-Activated

## 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)###### Pretest probability financial definition of pretest probability

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###### Probability distribution

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###### Monkeying with Bayes theorem

###### Probability Density Function of the Intensity of a Laser Beam Reflected from a Location Target and Propagating Through...

###### Mark and recapture

Then the capture

**probability**P was defined as: P. =. 5. 10. f. q. +. 5. 90. (. 1. −. f. ). (. 1. −. q. ). ,. {\displaystyle P ... The capture**probability**refers to the**probability**of a detecting an individual animal or person of interest,[11] and has been ... where the first term refers to the**probability**of detection (capture**probability**) in a high risk zone, and the latter term ...**probability**q that a passenger with the disease came from such an area, where q,0.5), or low rates (**probability**1-q).[14] It ...**Probability** distribution

**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 ...

###### Wikipedia:Reference desk/Archives/Mathematics/2008 March 12

Thus, we now sum these

**probabilities**: P. =. 1. +. 1. +. 2. +. 6. +. 4. 35. =. 14. 35. =. 2. 5. {\displaystyle P={\dfrac {1+1+2+ ... And, therefore, the**probability**of at least 1 all-English quarter-final should be the sum of above two**probabilities**, i.e. 3. ... Q5 What's the**probability**of exactly 2 all-English semi-finals?. Q6 What's the**probability**of at least 1 all-English semi-final ... Question 6 - this is now easy, we just sum the**probabilities**of 1 and 2 english SFs. P. =. 2. 5. +. 1. 70. =. 29. 70. {\ ...###### Density (disambiguation)

**Probability**and measure theory[edit]. *

**Probability**density function, a function which maps

**probabilities**across the real line ... Kernel density estimation, used in statistics to estimate a

**probability**density function of a random variable ... Density estimation is the construction of an estimate of a

**probability**density function ...

###### Independence (**probability** theory)

if and only if their joint

**probability**equals the product of their**probabilities**: P. (. A. ∩. B. ). =. P. (. A. ). P. (. B. ). ... and**probability**densities f. X. (. x. ). {\displaystyle f_{X}(x)}. and f. Y. (. y. ). {\displaystyle f_{Y}(y)}. , are ... be a**probability**space and let A. {\displaystyle {\mathcal {A}}}. and B. {\displaystyle {\mathcal {B}}}. be two sub-σ-algebras ... Why this defines independence is made clear by rewriting with conditional**probabilities**: P. (. A. ∩. B. ). =. P. (. A. ). P. ( ...###### Mellin transform

In

**probability**theory[edit]. In**probability**theory, the Mellin transform is an essential tool in studying the distributions of ... The importance of the Mellin transform in**probability**theory lies in the fact that if X and Y are two independent random ...###### Ellipsoid

In

**probability**and statistics[edit]. The elliptical distributions, which generalize the multivariate normal distribution and ...###### Markov chain

These conditional

**probabilities**may be found by s. i. j. =. {. q. i. j. ∑. k. ≠. i. q. i. k. if i. ≠. j. 0. otherwise. .. {\ ... if both conditional**probabilities**are well defined, that is, if Pr. (. X. 1. =. x. 1. ,. …. ,. X. n. =. x. n. ). ,. 0.. {\ ... The**probability**of achieving X. 2. {\displaystyle X_{2}}. now depends on X. 1. {\displaystyle X_{1}}. ; for example, the state ... For example, if the Markov process is in state A, then the**probability**it changes to state E is 0.4, while the**probability**it ...###### Abraham de Moivre

He also produced the second textbook on

**probability**theory, The Doctrine of Chances: a method of calculating the**probabilities**... Zabell, S.L. (2005). Symmetry and Its Discontents: Essays on the History of Inductive**Probability**. New York City, New York, USA ...**Probability**[edit]. See also: de Moivre-Laplace theorem. De Moivre pioneered the development of analytic geometry and the theory ... De Moivre wrote a book on**probability**theory, The Doctrine of Chances, said to have been prized by gamblers. De Moivre first ...###### Gumbel distribution

and

**probability**density function f. (. x. ). =. e. −. (. x. +. e. −. x. ). .. {\displaystyle f(x)=e^{-(x+e^{-x})}.}. In this ... CumFreq, software for**probability**distribution fitting. [1] *^ Gumbel, E.J. (1954). Statistical theory of extreme values and ... In**probability**theory and statistics, the Gumbel distribution (Generalized Extreme Value distribution Type-I) is used to model ... Gumbel has also shown that the estimator r/(n+1) for the**probability**of an event - where r is the rank number of the observed ...###### Wikipedia:Reference desk/Archives/Mathematics/2007 September 20

Question: calculating

**probability**of two events occurring at same time. Answer: Please define the term "the same time".. May I ... Next if event B is completely independent of event A then you would expect the**probability**of both event A and event B ... If event A occurs 172 times in a 24 hour period (ie 172 time intervals which has event A) then the**probability**of event A in a ... if event B occurs 400 times (in a 24 hour period) the**probability**of event B in a time interval is 400/17280 = 0.023148. .. ...###### Bertrand paradox (**probability**)

... including frequentist

**probability**and subjectivist Bayesian**probability**.. Jaynes's solution using the "maximum ignorance" ... Joseph Bertrand introduced it in his work Calcul des probabilités (1889)[1] as an example to show that**probabilities**may not be ... To calculate the**probability**in question imagine the triangle rotated so a side is perpendicular to the radius. The chord is ... To calculate the**probability**in question imagine the triangle rotated so its vertex coincides with one of the chord endpoints. ...###### Centimorgan

The formula can be inverted, giving the distance in centimorgans as a function of the recombination

**probability**: d. =. 50. ln. ... The**probability**of recombination is approximately d/100 for small values of d and approaches 50% as d goes to infinity. ... Relation to the**probability**of recombination[edit]. Because genetic recombination between two markers is detected only if there ... the distance in centimorgans does not correspond exactly to the**probability**of genetic recombination. Assuming Haldane's map ...###### Promoter (genetics)

**Probability**of occurrence of each nucleotide[edit]. for -10 sequence T A T A A T 77% 76% 60% 61% 56% 82% for -35 sequence T T G ...

###### Self-serving bias

Self-awareness and

**probability**of improvement[edit]. The relationship between individuals' awareness levels and perceived ... However, they will engage in self-serving bias, attributing failure externally when they perceive a low**probability**of ... Individuals low in self-awareness will attribute failure externally regardless of their perceived**probability**of improvement. ... Individuals with high self-awareness attribute failure internally when they perceive a high**probability**of improvement. ...###### Borel-Cantelli lemma

Hence, the

**probability**of Xn = 0 occurring for infinitely many n is 0. Almost surely (i.e., with**probability**1), Xn is nonzero ... Let (En) be a sequence of events in some**probability**space and suppose that the sum of the**probabilities**of the En is finite. ... If the sum of the**probabilities**of the En is finite. ∑. n. =. 1. ∞. Pr. (. E. n. ). ,. ∞. ,. {\displaystyle \sum _{n=1}^{\infty ... Statement of lemma for**probability**spaces[edit]. Let E1,E2,... be a sequence of events in some**probability**space. The Borel- ...###### Pierre-Simon Laplace

The

**probability**that A will occur, given that B has occurred, is the**probability**of A and B occurring divided by the ... "Laplace took**probability**as an instrument for repairing defects in knowledge."[17] Laplace's work on**probability**and statistics ... He begins the text with a series of principles of**probability**, the first six being: ***Probability**is the ratio of the "favored ... When this is not true, we must first determine the**probabilities**of each event. Then, the**probability**is the sum of the ...###### Matrix (mathematics)

In

**probability**theory and statistics, stochastic matrices are used to describe sets of**probabilities**; for instance, they are ...**Probability**theory and statistics[edit]. Two different Markov chains. The chart depicts the number of particles (of a total of ... Beyond**probability**theory, they are applied in domains ranging from number theory to physics.[97][98] ... Stochastic matrices are square matrices whose rows are**probability**vectors, that is, whose entries are non-negative and sum up ...###### Integration by substitution

Denote this

**probability**P. (. Y. ∈. S. ). {\displaystyle P(Y\in S)}. . Of course, if Y. {\displaystyle Y}. has**probability**... with**probability**density p. X. {\displaystyle p_{X}}. and another random variable Y. {\displaystyle Y}. related to X. {\ ... Application in**probability**[edit]. Substitution can be used to answer the following important question in**probability**: given a ... what is the**probability**density for Y. {\displaystyle Y}. ? It is easiest to answer this question by first answering a slightly ...###### Lebesgue-Stieltjes integration

Riemann-Stieltjes integration and

**probability**theory[edit]. Where f is a continuous real-valued function of a real variable and ... This is particularly common in**probability**theory when v is the cumulative distribution function of a real-valued random ... They find common application in**probability**and stochastic processes, and in certain branches of analysis including potential ...###### Event (**probability** theory)

In

**probability**theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a**probability**is ... This is especially common in formulas for a**probability**, such as Pr. (. u. ,. X. ≤. v. ). =. F. (. v. ). −. F. (. u. ). .. {\ ... For the standard tools of**probability**theory, such as joint and conditional**probabilities**, to work, it is necessary to use a σ- ... with**probability**zero) and the sample space itself (a certain event, with**probability**one). Other events are proper subsets of ...###### Contraposition

the prior

**probability**) of P. {\displaystyle P}. . The pair of inverted conditional opinions is denoted (. ω. P. ,. ~. Q. A. ,. ... the prior**probability**) of P. {\displaystyle P}. . Assume that Pr. (. ¬. Q. ∣. P. ). =. 1. {\displaystyle \Pr(\lnot Q\mid P)=1} ... In the equation above the conditional**probability**Pr. (. ¬. Q. ∣. P. ). {\displaystyle \Pr(\lnot Q\mid P)}. generalizes the ... i.e. in addition to assigning TRUE or FALSE we can also assign any**probability**to the statement. The term a. (. P. ). {\ ...###### Monty Hall problem

**Probability**1/3. (100 out of 300)

**Probability**1/6. (50 out of 300)

**Probability**1/6. (50 out of 300)

**Probability**1/3. (100 out ... Many

**probability**text books and articles in the field of

**probability**theory derive the conditional

**probability**solution through ... What is the

**probability**of winning the car by always switching?. *What is the

**probability**of winning the car given the player ... Conditional

**probability**by direct calculation[edit]. Tree showing the

**probability**of every possible outcome if the player ...

###### Failure mode and effects analysis

Risk is the combination of End Effect

**Probability**And Severity where**probability**and severity includes the effect on non- ...**Probability**. The likelihood of the failure occurring.. Risk Priority Number (RPN). Severity (of the event) ×**Probability**(of ...**Probability**(P)[edit]. It is necessary to look at the cause of a failure mode and the likelihood of occurrence. This can be ... P)**Probability**(estimate) (S) Severity (D) Detection (Indications to Operator, Maintainer) Detection Dormancy Period Risk Level ...###### Probabilistic classification

they assign

**probabilities**to all y. ∈. Y. {\displaystyle y\in Y}. (and these**probabilities**sum to one). "Hard" classification ... I]n data mining applications the interest is often more in the class**probabilities**p. ℓ. (. x. ). ,. ℓ. =. 1. ,. …. ,. K. {\ ... "**Probability**calibration". jmetzen.github.io. Retrieved 2019-06-18.. *^ Platt, John (1999). "Probabilistic outputs for support ... Some models, such as logistic regression, are conditionally trained: they optimize the conditional**probability**Pr. (. Y. ,. X. ...###### Polyclonal B cell response

Increased

**probability**of recognizing any antigen[edit]. If an antigen can be recognized by more than one component of its ... Although the polyclonal response confers advantages on the immune system, in particular, greater**probability**of reacting ...###### Hardy-Weinberg principle

Multinomial distribution (Hardy-Weinberg is a trinomial distribution with

**probabilities**(. θ. 2. ,. 2. θ. (. 1. −. θ. ). ,. (. ... For example, the**probability**of the mating combination (AA,aa) is 2 ft(AA)ft(aa) and it can only result in the Aa genotype: [0, ... and conditional**probability**. For example, consider the**probability**of an offspring from the generation t. {\displaystyle \ ... Fisher's exact test (**probability**test)[edit]. Fisher's exact test can be applied to testing for Hardy-Weinberg proportions. ...**Probability** distribution fitting

being the cumulative

**probability**, i.e. the**probability**that the data value is less than X. {\displaystyle X}. . Thus, using the ...**Probability**distribution fitting or simply distribution fitting is the fitting of a**probability**distribution to a series of ... There are many**probability**distributions (see list of**probability**distributions) of which some can be fitted more closely to ... depending on the selected**probability**distribution. In this method the cumulative**probability**needs to be estimated by the ...###### Genetic drift

...

**probability**(**probability**of a given allele being present) is 1/2 (i.e., the**probability**that there are k copies of A (or B) ... The**probability**that each of the four survivors has a given allele is 1/2, and so the**probability**that any particular allele ... and the**probability**of this combination is 6/16. The total number of other combinations is ten, so the**probability**of unequal ... then given unlimited time the**probability**A will ultimately become fixed in the population is 75% and the**probability**that B ...###### Bias of an estimator

"Lectures on

**probability**theory and mathematical statistics".. *^ DeGroot, Morris H. (1986).**Probability**and Statistics (2nd ed ... Estimating a Poisson**probability**[edit]. A far more extreme case of a biased estimator being better than any unbiased estimator ... One consequence of adopting this prior is that S2/σ2 remains a pivotal quantity, i.e. the**probability**distribution of S2/σ2 ... when the expectation is taken over the**probability**distribution of σ2 given S2, as it is in the Bayesian case, rather than S2 ...**Probability** distribution - Wikipedia

**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** - Wikipedia

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 ...###### Coverage **probability** - Wikipedia

The "nominal coverage

**probability**" is often set at 0.95. The coverage**probability**is the actual**probability**that the interval ... the nominal coverage**probability**will equal the coverage**probability**(termed "true" or "actual" coverage**probability**for ... The "**probability**" in coverage**probability**is interpreted with respect to a set of hypothetical repetitions of the entire data ... When the actual coverage**probability**is greater than the nominal coverage**probability**, the interval is termed "conservative", ...**Probability** measure - Wikipedia

In mathematics, a

**probability**measure is a real-valued function defined on a set of events in a**probability**space that ... The requirements for a function μ to be a**probability**measure on a**probability**space are that: μ must return results in the ...**Probability**measures are also used in mathematical biology. For instance, in comparative sequence analysis a**probability**... is that a**probability**measure must assign value 1 to the entire**probability**space. Intuitively, the additivity property says ...**Probability** theory

... 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, ...###### Re: **Probability**

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 ...###### Compound **Probability**

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 ...###### Subjective **Probability**

... 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 ...###### Non-**probability** Sampling | SurveyMonkey

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 ...###### Induction without **Probability**

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 ...###### Answers about **Probability**

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, ...###### Odds | **probability** | Britannica

###### Progress in **Probability**

... 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 ...###### Answers about **Probability**

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. ?. ...**Probability**

... 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 ...**Probability**

**Probability** of Causation | NIOSH | CDC

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 " ...**Probability** of Causation | NIOSH | CDC

... 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 ...**Probability** and Its Applications

... 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 ...**Probability** and Distributions | SpringerLink

... 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 ...**probability** distribution | Encyclopedia.com

... 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 ...**Probability** Model | Encyclopedia.com

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 ...**Probability** Intro

**Probability** theory

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** distribution

**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, ...

**Probability**-Distributions on the App Store

... and learn more about

**Probability**-Distributions. Download**Probability**-Distributions and enjoy it on your iPhone, iPad, and iPod ... Compute**probabilities**, determine percentiles, and plot the**probability**density function for the normal (Gaussian), t, chi- ... Compute**probabilities**, approximate percentiles, and plot the**probability**mass function for the binomial, geometric, ... To download the free app**Probability**-Distributions by Matthew Bognar, get iTunes now. ...**Probability** Theory - Cambridge University Press

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 ...###### Category:**Probability** theory - Wikimedia Commons

... 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); ...###### Impossible event | **probability** theory | Britannica

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 ...###### PHP: SVMModel::predict **probability** - Manual

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 ...DistributionsStochastic processesIntroduction to ProbabilityConditionalOutcomesDensityMathematical Statistics2017PhenomenaCalculate the probabilityLikelihoodConcept of probabilityApplications of probabilityFractionsContinuous probabilityEmpiricalStatisticalOccurBasic probabilityTotal ProbabilityCompute the probabilityDevelopment of probability theorySearchCoinDescribesOutcomePosterior ProbabilityUnivariateBinomialCalculusStatisticiansOccurrenceSubjective probabilityTheoreticalRules of probabilityNature of probabilityBasics of probabilityShows the probabilityHigher the probabilityPercent and probabilityAnalysis and ProbabilityDetermine the probabilityMathematics of probabilityApplication of probabilityStatistics and ProbabilityInterpretation of probabilityDiceGaussianPracticeISSNProcessesPhysicsRandomDistributionExercisesRelative frequencyTrue probability

###### Distributions19

- 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)
- Identifying Probability Distributions In Exercises 11-14, determine whether the table represents a probability distribution. (bartleby.com)

###### Stochastic processes3

- 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)

###### Introduction to Probability3

- 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)

###### Conditional4

- 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)

###### Outcomes8

- 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)

###### Density2

- 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)

###### Mathematical Statistics3

- 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)

###### 20171

- Receive email alerts on new books, offers and news in Statistics & Probability 2017 Catalogue. (cambridge.org)

###### Phenomena4

- 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)

###### Calculate the probability3

- 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)
- Bowl a strike as you calculate the probability of knocking down pins! (education.com)

###### Likelihood11

- 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)

###### Concept of probability2

- 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)

###### Applications of probability3

- 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)

###### Fractions5

- 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)
- #Trigonometry # Probability #Area #BasicOperations #QuadraticFormula #Percentages , #Fractions , #Decimals #Graphicalinterpretation #Formula Speak to us. (twitter.com)

###### Continuous probability2

- The normal distribution is a commonly encountered continuous probability distribution. (wikipedia.org)
- Key topics covered include:* Random variables and most of their frequently used discrete and continuous probability distribution function. (worldcat.org)

###### Empirical6

- 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)

###### Statistical8

- 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)

###### Occur10

- 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)

###### Basic probability3

- 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)

###### Total Probability2

- Total probability is 15/64. (answers.com)
- Since there are 10 such minutes during a day, the total probability per day is 0.0001. (usingenglish.com)

###### Compute the probability2

###### Development of probability theory1

- 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)

###### Search1

- 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)

###### Coin9

- 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)

###### Describes5

- 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)
- He takes complex concepts and describes them in understandable language, provides realistic applications that highlight the far-extending reaches of probability, and engages the problem-solving intuitions that lie at the heart of mathematics. (princeton.edu)

###### Outcome10

- 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)
- Associates a particulare probability of occurrence with each outcome in the sample space. (answers.com)
- The probability for a given event can be thought of as the ratio of the number of ways that event can happen divided by the number of ways that any possible outcome could happen. (gsu.edu)
- If you allow the outcome x to take a continuous range of values, then the probability P(x) takes a different character, since to get a finite result for probability, you must sum the probability over a finite range of x. (gsu.edu)
- In observational studies, the probability of exposure can depend on external factors (called confounders) that also affect the outcome. (bmj.com)
- Students will recognize that the probability of an outcome can be estimated from the long-run relative frequencies. (ti.com)
- The probability of an outcome can be 2/1. (ti.com)
- If an outcome is sure to happen, the probability of the outcome is 1. (ti.com)
- Students explore how they can use probability to help choose a winning outcome. (ti.com)
- Be sure students explain how they know which outcome is more likely in each of the simulations and how they might describe the probability of each. (ti.com)

###### Posterior Probability1

- Posterior probability is the revised probability of an event occurring after taking into consideration new information. (investopedia.com)

###### Univariate1

- 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)

###### Binomial1

- The construction of binomial confidence intervals is a classic example where coverage probabilities rarely equal nominal levels. (wikipedia.org)

###### Calculus1

- But if the number of events is very large, as in the distribution of energy among the molecules of a gas, then the probability can be approximated by a continuous variable so that the methods of calculus can be used. (gsu.edu)

###### Statisticians2

- 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)

###### Occurrence2

- 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)
- 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)

###### Subjective probability6

- What Is Subjective Probability? (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)
- Subjective Probability - The Real Thing Any thoughts on whether they are good for beginners? (twitter.com)

###### Theoretical6

- 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)
- 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)
- In The Probability Lifesaver , Miller does more than simply present the theoretical framework of probability. (princeton.edu)
- A balanced mix of theoretical and practical problem-solving approaches in probability-suited for personal study as well as textbook reading in and out of the classroom. (princeton.edu)

###### Rules of probability1

- The standard rules of probability can be interpreted as uniquely valid principles in logic. (cambridge.org)

###### Nature of probability1

- 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)

###### Basics of probability2

- 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)

###### Shows the probability1

- 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)

###### Higher the probability1

- # 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)

###### Percent and probability1

- percent and probability? (yahoo.com)

###### Analysis and Probability1

- 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)

###### Determine the probability2

###### Mathematics of probability2

- This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. (cambridge.org)
- This book helped me understand the big questions behind the mathematics of probability: why the complex theories I was learning are true, where they come from, and what are their applications. (princeton.edu)

###### Application of probability1

- For application of probability to physical processes, the use of the distribution function is a very useful strategy. (gsu.edu)

###### Statistics and Probability1

- What do statistics and probability reveal about the natural world? (edrants.com)

###### Interpretation of probability1

- Particularly when the frequency interpretation of probability is mistakenly assumed to be the only possible basis for frequentist inference . (wikipedia.org)

###### Dice6

- The probability mass function (pmf) p ( S ) specifies the probability distribution for the sum S of counts from two dice . (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)
- Calculate the mathematical probability of getting a sum higher than 18 for each combination of dice when rolling them 100 times. (scientificamerican.com)
- Probability can be as easy as rolling dice! (education.com)

###### Gaussian1

- The simplest probability model is the Gaussian, or normal, distribution, of which there are many examples in biology, medicine, and public health . (encyclopedia.com)

###### Practice7

- 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)

###### ISSN1

- From July 2014 series continued as 'Probability Theory and Stochastic Modelling' PTSM (ISSN 2199-3130). (springer.com)

###### Processes1

- A resource for probability AND random processes, with hundreds of worked examples and probability and Fourier transform tablesThis survival guide in probability and random processes eliminates the need to pore through several resources to find a certain formula or table. (worldcat.org)

###### Physics3

- 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)

###### Random12

- In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events . (wikipedia.org)
- a multivariate distribution (a joint probability distribution ) gives the probabilities of a random vector - a list of two or more random variables - taking on various combinations of values. (wikipedia.org)
- In the frequentist interpretation, probabilities are discussed only when dealing with well-defined random experiments (or random samples). (wikipedia.org)
- This may seem like a random probability sampling design, but consider this: there's probably a difference between the type of people who can come to your store in the morning versus those who have to visit later. (surveymonkey.com)
- 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 . (mcgill.ca)
- A random variable then defines a probability measure on the sample space by assigning a subset of the sample space the probability of its inverse image in the state space. (mcgill.ca)
- if grapefruits in an orchard are normally distributed with a mean of 5.93 in and sd of 0.59i what % of them are larger than 5.88 in a random sample of 100 grapefruits from the same orchard and the mean diameter is calculated what is the probability that the sample mean is greater than 5.88 in Thank you. (yahoo.com)
- This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). (repec.org)
- Your child will learn to find the probability of picking a random day on the calendar. (education.com)
- This enrichment uses a characterization of the laws of random variables in a probability space in terms of symmetries of the expectation. (ubc.ca)
- This talk is focused on the commutative case, where the laws of random variables are also described in terms of certain affinely flat structures on the formal moduli space of a naturally defined family attached to the given algebraic probability space, which the relevant category is the homotopy category of \(L_\infty\)-algebras. (ubc.ca)
- We introduce the notion of almost automorphic random functions in probability. (hindawi.com)

###### Distribution17

- A discrepancy between the coverage probability and the nominal coverage probability frequently occurs when approximating a discrete distribution with a continuous one. (wikipedia.org)
- 9) = 1/12 + 1/18 + 1/36 = 1/6, and all other probabilities in the distribution. (wikipedia.org)
- The total area under the curve is 1, so it's a valid probability distribution. (mail-archive.com)
- For any segment of the real line, you can determine exactly what the probability will be that a point will fall on it--even though the distribution extends forever. (mail-archive.com)
- The fact that there's an infinite number of choices doesn't mean that those choices can't be normalized to a probability distribution. (mail-archive.com)
- push forward measure of the probability distribution on the state space. (mcgill.ca)
- A probability distribution is called discrete if its cumulative distribution function only increases in jumps. (mcgill.ca)
- The support of a distribution is the smallest closed set whose complement has probability zero. (mcgill.ca)
- From a table of the standard normal distribution, you can see that the probability of a value greater than 5.88 is 0.5338 so 53.38% of the grapefruit will be larger than 5.88 inches. (yahoo.com)
- Because the normal distribution is symmetrical, the cumulative probability from - infinity to Z = 0.0847 is the same as the cumulative probability from Z = -0.0847 to infinity. (yahoo.com)
- Create a default normal probability distribution object. (mathworks.com)
- Probability distribution, specified as a probability distribution object. (mathworks.com)
- Hi, bu1234-ga: In the simplest case the 'probability space' for a continuous uniform distribution would be a finite interval of real numbers, but the idea of a uniform distribution could be easily extended to any bounded, measurable open subset of a higher-dimensional space, e.g. a ball of finite radius in 3 dimensions. (google.com)
- The following functions are used to retrieve information or perform another function on a probability distribution. (maplesoft.com)
- If it is a probability distribution, sketch its graph. (bartleby.com)
- If it is not a probability distribution, state any properties that are not satisfied. (bartleby.com)
- Whether the provided data represents the probability distribution or not and also draw the graph if it is a probability distribution and give a property if it is not. (bartleby.com)

###### Exercises1

- Probability is not a spectator sport, so the book contains almost 450 exercises to challenge the reader and to deepen their understanding. (psu.edu)

###### Relative frequency2

- it defines an event's probability as the limit of its relative frequency in a large number of trials. (wikipedia.org)
- Mathematical probability is the measure of the relative frequency of an event occurring. (calvin.edu)

###### True probability2

- 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)