###### Probability Theory

###### Probability Learning

###### Models, Statistical

###### Bayes Theorem

###### Algorithms

###### Computer Simulation

###### Markov Chains

###### Models, Genetic

###### Monte Carlo Method

###### Models, Biological

###### Models, Theoretical

###### Stochastic Processes

###### Likelihood Functions

###### Data Interpretation, Statistical

###### Ion Channel Gating

###### Predictive Value of Tests

###### Decision Theory

###### Sensitivity and Specificity

###### Risk Factors

###### Reproducibility of Results

###### Decision Support Techniques

###### Treatment Outcome

###### Patch-Clamp Techniques

###### Logistic Models

###### Retrospective Studies

###### Nomograms

###### Prospective Studies

###### Membrane Potentials

###### Statistical Distributions

###### Survival Analysis

###### Prognosis

###### Risk Assessment

###### Cost-Benefit Analysis

###### Age Factors

###### Choice Behavior

###### ROC Curve

###### Follow-Up Studies

###### Uncertainty

###### Electrophysiology

###### Cohort Studies

###### Software

###### Synaptic Transmission

###### Quality-Adjusted Life Years

###### Decision Trees

###### Synapses

###### Regression Analysis

###### Models, Neurological

###### Decision Making

###### Multivariate Analysis

###### Mutation

###### Computational Biology

###### Mathematics

###### Excitatory Postsynaptic Potentials

###### Calcium

###### 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

###### Incidence

###### Ventilation-Perfusion Ratio

###### Presynaptic Terminals

###### Pregnancy

###### Entropy

###### Proportional Hazards Models

###### Bias (Epidemiology)

###### Life Tables

###### Poisson Distribution

###### Biometry

###### Sex Factors

###### Reward

###### Pattern Recognition, Automated

###### Biological Evolution

###### Confidence Intervals

###### Biostatistics

###### Databases, Factual

###### False Positive Reactions

###### Selection, Genetic

###### Genetic Markers

###### Reinforcement Schedule

###### Disease-Free Survival

###### Severity of Illness Index

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

###### Odds Ratio

###### Gene Frequency

###### Epithelial Sodium Channels

###### Research Design

###### Evolution, Molecular

###### Molecular Sequence Data

###### Cross-Sectional Studies

###### Kaplan-Meier Estimate

###### Calcium Channels

###### Health Surveys

###### Forecasting

###### Photic Stimulation

###### Longitudinal Studies

###### Linear Models

###### Cluster Analysis

###### Disease Progression

###### Evoked Potentials

###### Artificial Intelligence

###### Pedigree

###### Questionnaires

###### Ecosystem

###### Models, Psychological

###### Socioeconomic Factors

###### Sequence Analysis, Protein

###### Epidemiologic Methods

###### Neuronal Plasticity

###### Magnetic Resonance Imaging

###### Geography

###### Proteins

###### Sequence Alignment

###### Genetic Linkage

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

###### Mathematical Computing

###### Demography

###### Bone Marrow Transplantation

###### Actuarial Analysis

###### Nonlinear Dynamics

###### Life Expectancy

###### Chromosome Mapping

###### Sodium Channels

###### Fibrin Fibrinogen Degradation Products

###### HIV Infections

###### Neural Networks (Computer)

###### Sequence Analysis, DNA

###### Health Care Costs

###### Game Theory

###### Combined Modality Therapy

###### Statistics, Nonparametric

###### Neoplasm Staging

###### Information Theory

###### Data Collection

###### Transplantation, Homologous

###### Remission Induction

###### Neoplasms

###### Randomized Controlled Trials as Topic

###### Diagnosis, Computer-Assisted

###### Hippocampus

###### Models, Molecular

###### Fertility

###### Phenotype

###### Base Sequence

###### Area Under Curve

###### Diagnosis

###### Oocytes

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

###### Breeding

###### Electroencephalography

###### Age Distribution

###### Heterozygote

###### Spain

###### Registries

###### Mass Screening

###### Neoplasm Recurrence, Local

###### Case-Control Studies

###### Ryanodine Receptor Calcium Release Channel

###### 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)**Recurrence**is a term used to describe the return or re-occurrence of a condition, symptom, or disease after it has been treated or gone into remission. This can be a common occurrence with certain types of illnesses or conditions, such as cancer, where the cancer cells may still be present in the body after treatment and can grow and cause new tumors.

Recurrence can also refer to the re-emergence of symptoms in a previously treated condition, such as a chronic pain condition that returns after a period of remission.

In medical research, recurrence is often studied to understand the underlying causes of disease progression and to develop new treatments and interventions to prevent or delay its return.

**Pulmonary embolism**is a type of blood clot that forms in the lungs and can be fatal if not treated promptly. It occurs when a blood clot, usually from the legs, travels to the lungs and blocks one or more of the arteries in the lung. This can cause damage to the lung tissue and reduce the amount of oxygen that reaches the heart and other organs.

The symptoms of pulmonary embolism can vary, but may include shortness of breath, chest pain, coughing up blood, rapid heart rate, and fever. In some cases, the clot may be large enough to cause a pulmonary infarction (a " lung injury" caused by lack of oxygen), which can lead to respiratory failure and death.

Pulmonary embolism can be diagnosed with imaging tests such as chest X-rays, CT scans, and ultrasound. Treatment typically involves medications to dissolve the clot or prevent new ones from forming, and in some cases, surgery may be necessary to remove the clot.

Preventive measures include:

* Avoiding prolonged periods of immobility, such as during long-distance travel

* Exercising regularly to improve circulation

* Managing chronic conditions such as high blood pressure and cancer

* Taking blood-thinning medications to prevent clot formation

Early recognition and treatment of pulmonary embolism are critical to reduce the risk of complications and death.

**Breast Neoplasms**also known as Breast Cancer, is a condition where abnormal cell growth develops in the breast tissue. It originates from various cell types including milk-producing glands (lobules), milk ducts, connective tissue, and fatty or fibrous tissue.

There are different types of Breast Neoplasms such as:

1. Fibroadenomas: These are benign tumors that are made up of glandular and fibrous tissues. They are usually small and round, with a smooth surface, and can be moved easily under the skin.

2. Cysts: These are fluid-filled sacs that can develop in both breast tissue and milk ducts. They are usually benign and can disappear on their own or be drained surgically.

3. Ductal Carcinoma In Situ (DCIS): This is a precancerous condition where abnormal cells grow inside the milk ducts. If left untreated, it can progress to invasive breast cancer.

4. Invasive Ductal Carcinoma (IDC): This is the most common type of breast cancer and starts in the milk ducts but grows out of them and invades surrounding tissue.

5. Invasive Lobular Carcinoma (ILC): It originates in the milk-producing glands (lobules) and grows out of them, invading nearby tissue.

Breast Neoplasms can cause various symptoms such as a lump or thickening in the breast or underarm area, skin changes like redness or dimpling, change in size or shape of one or both breasts, discharge from the nipple, and changes in the texture or color of the skin.

Treatment options for Breast Neoplasms may include surgery such as lumpectomy, mastectomy, or breast-conserving surgery, radiation therapy which uses high-energy beams to kill cancer cells, chemotherapy using drugs to kill cancer cells, targeted therapy which uses drugs or other substances to identify and attack cancer cells while minimizing harm to normal cells, hormone therapy, immunotherapy, and clinical trials.

It is important to note that not all Breast Neoplasms are cancerous; some are benign (non-cancerous) tumors that do not spread or grow.

**Disease progression**refers to the natural course or worsening of a disease over time, often accompanied by changes in symptoms, physical signs, and laboratory test results. It can be a gradual process or may occur suddenly, and is influenced by various factors such as genetics, lifestyle, environment, and medical treatment.

Disease progression can be classified into several types based on the pattern of worsening:

1. Chronic progressive disease: In this type, the disease worsens steadily over time, with a gradual increase in symptoms and decline in function. Examples include rheumatoid arthritis, osteoarthritis, and Parkinson's disease.

2. Acute progressive disease: This type of disease worsens rapidly over a short period, often followed by periods of stability. Examples include sepsis, acute myocardial infarction (heart attack), and stroke.

3. Cyclical disease: In this type, the disease follows a cycle of worsening and improvement, with periodic exacerbations and remissions. Examples include multiple sclerosis, lupus, and rheumatoid arthritis.

4. Recurrent disease: This type is characterized by episodes of worsening followed by periods of recovery. Examples include migraine headaches, asthma, and appendicitis.

5. Catastrophic disease: In this type, the disease progresses rapidly and unpredictably, with a poor prognosis. Examples include cancer, AIDS, and organ failure.

Disease progression can be influenced by various factors, including:

1. Genetics: Some diseases are inherited and may have a predetermined course of progression.

2. Lifestyle: Factors such as smoking, lack of exercise, and poor diet can contribute to disease progression.

3. Environmental factors: Exposure to toxins, allergens, and other environmental stressors can influence disease progression.

4. Medical treatment: The effectiveness of medical treatment can impact disease progression, either by slowing or halting the disease process or by causing unintended side effects.

5. Co-morbidities: The presence of multiple diseases or conditions can interact and affect each other's progression.

Understanding the type and factors influencing disease progression is essential for developing effective treatment plans and improving patient outcomes.

**HIV Infections**Medical Definition

HIV (human immunodeficiency virus) infection is a condition in which the body is infected with HIV, a type of retrovirus that attacks the body's immune system. HIV infection can lead to AIDS (acquired immunodeficiency syndrome), a condition in which the immune system is severely damaged and the body is unable to fight off infections and diseases.

There are several ways that HIV can be transmitted, including:

1. Sexual contact with an infected person

2. Sharing of needles or other drug paraphernalia with an infected person

3. Mother-to-child transmission during pregnancy, childbirth, or breastfeeding

4. Blood transfusions ( although this is rare in developed countries due to screening processes)

5. Organ transplantation (again, rare)

The symptoms of HIV infection can be mild at first and may not appear until several years after infection. These symptoms can include:

1. Fever

2. Fatigue

3. Swollen glands in the neck, armpits, and groin

4. Rash

5. Muscle aches and joint pain

6. Night sweats

7. Diarrhea

8. Weight loss

If left untreated, HIV infection can progress to AIDS, which is a life-threatening condition that can cause a wide range of symptoms, including:

1. Opportunistic infections (such as pneumocystis pneumonia)

2. Cancer (such as Kaposi's sarcoma)

3. Wasting syndrome

4. Neurological problems (such as dementia and seizures)

HIV infection is diagnosed through a combination of blood tests and physical examination. Treatment typically involves antiretroviral therapy (ART), which is a combination of medications that work together to suppress the virus and slow the progression of the disease.

Prevention methods for HIV infection include:

1. Safe sex practices, such as using condoms and dental dams

2. Avoiding sharing needles or other drug-injecting equipment

3. Avoiding mother-to-child transmission during pregnancy, childbirth, or breastfeeding

4. Post-exposure prophylaxis (PEP), which is a short-term treatment that can prevent infection after potential exposure to the virus

5. Pre-exposure prophylaxis (PrEP), which is a daily medication that can prevent infection in people who are at high risk of being exposed to the virus.

It's important to note that HIV infection is manageable with proper treatment and care, and that people living with HIV can lead long and healthy lives. However, it's important to be aware of the risks and take steps to prevent transmission.

**Acute disease**s are medical conditions that have a sudden onset and a short duration. They are usually self-limiting, meaning they do not persist over time unless left untreated. Acute diseases can be caused by a variety of factors, such as viral or bacterial infections, allergic reactions, or physical injuries.

Examples of acute diseases include:

1. Common cold and flu

2. Pneumonia and bronchitis

3. Appendicitis and other abdominal emergencies

4. Heart attacks and strokes

5. Asthma attacks and allergic reactions

6. Skin infections and cellulitis

7. Urinary tract infections

8. Sinusitis and meningitis

9. Gastroenteritis and food poisoning

10. Sprains, strains, and fractures.

Acute diseases can be treated effectively with antibiotics, medications, or other therapies. However, if left untreated, they can lead to chronic conditions or complications that may require long-term care. Therefore, it is important to seek medical attention promptly if symptoms persist or worsen over time.

**Neoplasms**Medical Definition

Neoplasm refers to an abnormal growth of cells that can be benign (non-cancerous) or malignant (cancerous). Neoplasms can occur in any part of the body and can affect various organs and tissues. The term "neoplasm" is often used interchangeably with "tumor," but while all tumors are neoplasms, not all neoplasms are tumors.

Types of Neoplasms

There are many different types of neoplasms, including:

1. Carcinomas: These are malignant tumors that arise in the epithelial cells lining organs and glands. Examples include breast cancer, lung cancer, and colon cancer.

2. Sarcomas: These are malignant tumors that arise in connective tissue, such as bone, cartilage, and fat. Examples include osteosarcoma (bone cancer) and soft tissue sarcoma.

3. Lymphomas: These are cancers of the immune system, specifically affecting the lymph nodes and other lymphoid tissues. Examples include Hodgkin lymphoma and non-Hodgkin lymphoma.

4. Leukemias: These are cancers of the blood and bone marrow that affect the white blood cells. Examples include acute myeloid leukemia (AML) and chronic lymphocytic leukemia (CLL).

5. Melanomas: These are malignant tumors that arise in the pigment-producing cells called melanocytes. Examples include skin melanoma and eye melanoma.

Causes and Risk Factors of Neoplasms

The exact causes of neoplasms are not fully understood, but there are several known risk factors that can increase the likelihood of developing a neoplasm. These include:

1. Genetic predisposition: Some people may be born with genetic mutations that increase their risk of developing certain types of neoplasms.

2. Environmental factors: Exposure to certain environmental toxins, such as radiation and certain chemicals, can increase the risk of developing a neoplasm.

3. Infection: Some neoplasms are caused by viruses or bacteria. For example, human papillomavirus (HPV) is a common cause of cervical cancer.

4. Lifestyle factors: Factors such as smoking, excessive alcohol consumption, and a poor diet can increase the risk of developing certain types of neoplasms.

5. Family history: A person's risk of developing a neoplasm may be higher if they have a family history of the condition.

Signs and Symptoms of Neoplasms

The signs and symptoms of neoplasms can vary depending on the type of cancer and where it is located in the body. Some common signs and symptoms include:

1. Unusual lumps or swelling

2. Pain

3. Fatigue

4. Weight loss

5. Change in bowel or bladder habits

6. Unexplained bleeding

7. Coughing up blood

8. Hoarseness or a persistent cough

9. Changes in appetite or digestion

10. Skin changes, such as a new mole or a change in the size or color of an existing mole.

Diagnosis and Treatment of Neoplasms

The diagnosis of a neoplasm usually involves a combination of physical examination, imaging tests (such as X-rays, CT scans, or MRI scans), and biopsy. A biopsy involves removing a small sample of tissue from the suspected tumor and examining it under a microscope for cancer cells.

The treatment of neoplasms depends on the type, size, location, and stage of the cancer, as well as the patient's overall health. Some common treatments include:

1. Surgery: Removing the tumor and surrounding tissue can be an effective way to treat many types of cancer.

2. Chemotherapy: Using drugs to kill cancer cells can be effective for some types of cancer, especially if the cancer has spread to other parts of the body.

3. Radiation therapy: Using high-energy radiation to kill cancer cells can be effective for some types of cancer, especially if the cancer is located in a specific area of the body.

4. Immunotherapy: Boosting the body's immune system to fight cancer can be an effective treatment for some types of cancer.

5. Targeted therapy: Using drugs or other substances to target specific molecules on cancer cells can be an effective treatment for some types of cancer.

Prevention of Neoplasms

While it is not always possible to prevent neoplasms, there are several steps that can reduce the risk of developing cancer. These include:

1. Avoiding exposure to known carcinogens (such as tobacco smoke and radiation)

2. Maintaining a healthy diet and lifestyle

3. Getting regular exercise

4. Not smoking or using tobacco products

5. Limiting alcohol consumption

6. Getting vaccinated against certain viruses that are associated with cancer (such as human papillomavirus, or HPV)

7. Participating in screening programs for early detection of cancer (such as mammograms for breast cancer and colonoscopies for colon cancer)

8. Avoiding excessive exposure to sunlight and using protective measures such as sunscreen and hats to prevent skin cancer.

It's important to note that not all cancers can be prevented, and some may be caused by factors that are not yet understood or cannot be controlled. However, by taking these steps, individuals can reduce their risk of developing cancer and improve their overall health and well-being.

**Prostatic Neoplasms**are tumors that occur in the prostate gland, which is a small gland located below the bladder in males. These neoplasms can be benign (non-cancerous) or malignant (cancerous). Benign prostatic hyperplasia (BPH), also known as adenoma of the prostate, is the most common type of benign prostatic neoplasm, and it is not cancerous. It is a condition in which the prostate gland becomes enlarged, which can cause symptoms such as urinary hesitancy, weak stream, and frequent urination.

Malignant prostatic neoplasms are cancerous tumors that can be aggressive and spread to other parts of the body (metastasize). The most common type of malignant prostatic neoplasm is adenocarcinoma of the prostate, which accounts for approximately 95% of all prostate cancers. Other types of malignant prostatic neoplasms include sarcomas and small cell carcinomas.

Prostatic neoplasms can be diagnosed through a variety of tests such as digital rectal examination (DRE), prostate-specific antigen (PSA) test, imaging studies (ultrasound, CT scan or MRI), and biopsy. Treatment options for prostatic neoplasms depend on the type, stage, and grade of the tumor, as well as the patient's age and overall health. Treatment options can include active surveillance, surgery (robotic-assisted laparoscopic prostatectomy or open prostatectomy), radiation therapy (external beam radiation therapy or brachytherapy), and hormone therapy.

In summary, Prostatic Neoplasms are tumors that occur in the prostate gland, which can be benign or malignant. The most common types of malignant prostatic neoplasms are adenocarcinoma of the prostate, and other types include sarcomas and small cell carcinomas. Diagnosis is done through a variety of tests, and treatment options depend on the type, stage, and grade of the tumor, as well as the patient's age and overall health.

This definition of '**Neoplasm Recurrence, Local**' is from the Healthcare Professionals edition of the Merriam-Webster Medical Dictionary, copyright Â© 2007 by Merriam-Webster, Inc.

The diagnosis of GVHD is based on a combination of clinical findings, laboratory tests, and biopsies. Treatment options include immunosuppressive drugs, corticosteroids, and in severe cases, stem cell transplantation reversal or donor lymphocyte infusion.

Prevention of GVHD includes selecting the right donor, using conditioning regimens that minimize damage to the recipient's bone marrow, and providing appropriate immunosuppression after transplantation. Early detection and management of GVHD are critical to prevent long-term complications and improve survival rates.

**Genetic predisposition to disease**refers to the likelihood that an individual may develop a particular disease due to inherited genetic mutations or variations. These mutations or variations can increase the risk of developing certain diseases, but they do not guarantee that the individual will definitely develop the disease.

Explanation: Genetic predisposition to disease is influenced by multiple factors, including the presence of inherited genetic mutations or variations, environmental factors, and lifestyle choices. The likelihood of developing a particular disease can be increased by inherited genetic mutations that affect the functioning of specific genes or biological pathways. For example, inherited mutations in the BRCA1 and BRCA2 genes increase the risk of developing breast and ovarian cancer.

The expression of genetic predisposition to disease can vary widely, and not all individuals with a genetic predisposition will develop the disease. Additionally, many factors can influence the likelihood of developing a particular disease, such as environmental exposures, lifestyle choices, and other health conditions.

Inheritance patterns: Genetic predisposition to disease can be inherited in an autosomal dominant, autosomal recessive, or multifactorial pattern, depending on the specific disease and the genetic mutations involved. Autosomal dominant inheritance means that a single copy of the mutated gene is enough to cause the disease, while autosomal recessive inheritance requires two copies of the mutated gene. Multifactorial inheritance involves multiple genes and environmental factors contributing to the development of the disease.

Examples of diseases with a known genetic predisposition:

1. Huntington's disease: An autosomal dominant disorder caused by an expansion of a CAG repeat in the Huntingtin gene, leading to progressive neurodegeneration and cognitive decline.

2. Cystic fibrosis: An autosomal recessive disorder caused by mutations in the CFTR gene, leading to respiratory and digestive problems.

3. BRCA1/2-related breast and ovarian cancer: An inherited increased risk of developing breast and ovarian cancer due to mutations in the BRCA1 or BRCA2 genes.

4. Sickle cell anemia: An autosomal recessive disorder caused by a point mutation in the HBB gene, leading to defective hemoglobin production and red blood cell sickling.

5. Type 1 diabetes: An autoimmune disease caused by a combination of genetic and environmental factors, including multiple genes in the HLA complex.

Understanding the genetic basis of disease can help with early detection, prevention, and treatment. For example, genetic testing can identify individuals who are at risk for certain diseases, allowing for earlier intervention and preventive measures. Additionally, understanding the genetic basis of a disease can inform the development of targeted therapies and personalized medicine."

**Gambling**can be defined as the act of placing a bet or wagering money on an event with uncertain outcomes, with the intention of winning more money. This definition encompasses various forms of gambling, such as casino games like poker and slot machines, sports betting, lotteries, and online gambling.

Gambling can also be considered a behavioral addiction, as some individuals may become so consumed by the activity that they neglect other aspects of their lives, experience financial problems, and exhibit other signs of addiction. In this context, gambling is often classified as an impulse control disorder or a substance use disorder.

In the medical field, gambling can have various effects on an individual's physical and mental health, such as:

1. Financial problems: Gambling can lead to significant financial losses, which can cause stress, anxiety, and depression.

2. Sleep disturbances: Engaging in gambling activities at night or experiencing the excitement of winning can disrupt sleep patterns and lead to insomnia or other sleep disorders.

3. Substance abuse: Gambling can sometimes be accompanied by substance abuse, as individuals may turn to drugs or alcohol to cope with their gambling problems or to enhance their gambling experience.

4. Mood disorders: Gambling can contribute to the development of mood disorders such as depression, anxiety, and bipolar disorder.

5. Suicidal ideation: In extreme cases, individuals struggling with gambling addiction may experience suicidal thoughts or attempts.

6. Social problems: Gambling can strain relationships with family and friends, leading to social isolation and loneliness.

7. Physical health problems: Chronic stress and anxiety associated with gambling can contribute to various physical health problems, such as hypertension, cardiovascular disease, and musculoskeletal problems.

8. Cognitive impairment: Compulsive gambling can affect cognitive functioning, including attention, memory, and decision-making abilities.

9. Family dynamics: Gambling can have a significant impact on family dynamics, leading to conflicts, divorce, and financial hardship.

10. Financial consequences: Gambling can lead to significant financial problems, including debt, bankruptcy, and even criminal activity.

It's important to note that not all individuals who experience these problems will develop a gambling disorder, and that other factors such as genetics, family history, and environmental factors can contribute to the development of gambling addiction.

**chronic disease**is a condition that lasts for an extended period of time and requires ongoing management and care. Unlike acute diseases, which have a specific beginning and end, chronic diseases are long-term and often persistent, affecting daily life and activities. Examples of chronic diseases include diabetes, heart disease, arthritis, asthma, and cancer.

The burden of chronic diseases is significant, with over 70% of deaths worldwide attributed to them, according to the World Health Organization (WHO). In addition to the physical and emotional toll they take on individuals and their families, chronic diseases also pose a significant economic burden, accounting for a large proportion of healthcare expenditure.

In this article, we will explore the definition and impact of chronic diseases, as well as strategies for managing and living with them. We will also discuss the importance of early detection and prevention, as well as the role of healthcare providers in addressing the needs of individuals with chronic diseases.

What is a Chronic Disease?

A chronic disease is a condition that lasts for an extended period of time, often affecting daily life and activities. Unlike acute diseases, which have a specific beginning and end, chronic diseases are long-term and persistent. Examples of chronic diseases include:

1. Diabetes

2. Heart disease

3. Arthritis

4. Asthma

5. Cancer

6. Chronic obstructive pulmonary disease (COPD)

7. Chronic kidney disease (CKD)

8. Hypertension

9. Osteoporosis

10. Stroke

Impact of Chronic Diseases

The burden of chronic diseases is significant, with over 70% of deaths worldwide attributed to them, according to the WHO. In addition to the physical and emotional toll they take on individuals and their families, chronic diseases also pose a significant economic burden, accounting for a large proportion of healthcare expenditure.

Chronic diseases can also have a significant impact on an individual's quality of life, limiting their ability to participate in activities they enjoy and affecting their relationships with family and friends. Moreover, the financial burden of chronic diseases can lead to poverty and reduce economic productivity, thus having a broader societal impact.

Addressing Chronic Diseases

Given the significant burden of chronic diseases, it is essential that we address them effectively. This requires a multi-faceted approach that includes:

1. Lifestyle modifications: Encouraging healthy behaviors such as regular physical activity, a balanced diet, and smoking cessation can help prevent and manage chronic diseases.

2. Early detection and diagnosis: Identifying risk factors and detecting diseases early can help prevent or delay their progression.

3. Medication management: Effective medication management is crucial for controlling symptoms and slowing disease progression.

4. Multi-disciplinary care: Collaboration between healthcare providers, patients, and families is essential for managing chronic diseases.

5. Health promotion and disease prevention: Educating individuals about the risks of chronic diseases and promoting healthy behaviors can help prevent their onset.

6. Addressing social determinants of health: Social determinants such as poverty, education, and employment can have a significant impact on health outcomes. Addressing these factors is essential for reducing health disparities and improving overall health.

7. Investing in healthcare infrastructure: Investing in healthcare infrastructure, technology, and research is necessary to improve disease detection, diagnosis, and treatment.

8. Encouraging policy change: Policy changes can help create supportive environments for healthy behaviors and reduce the burden of chronic diseases.

9. Increasing public awareness: Raising public awareness about the risks and consequences of chronic diseases can help individuals make informed decisions about their health.

10. Providing support for caregivers: Chronic diseases can have a significant impact on family members and caregivers, so providing them with support is essential for improving overall health outcomes.

Conclusion

Chronic diseases are a major public health burden that affect millions of people worldwide. Addressing these diseases requires a multi-faceted approach that includes lifestyle changes, addressing social determinants of health, investing in healthcare infrastructure, encouraging policy change, increasing public awareness, and providing support for caregivers. By taking a comprehensive approach to chronic disease prevention and management, we can improve the health and well-being of individuals and communities worldwide.

**Precursor Cell Lymphoblastic Leukemia-Lymphoma**(Pre-B ALL) is a type of cancer that affects the blood and bone marrow. It is a form of acute lymphoblastic leukemia (ALL), which is a rare and aggressive cancer of the immune system.

Pre-B ALL is characterized by the abnormal growth of immature white blood cells called B lymphocytes. These cells are produced in the bone marrow and are normally present in the blood. In Pre-B ALL, the abnormal B cells accumulate in the bone marrow, blood, and other organs, crowding out normal cells and causing a variety of symptoms.

The symptoms of Pre-B ALL can vary depending on the individual patient, but may include:

* Fatigue

* Easy bruising or bleeding

* Frequent infections

* Swollen lymph nodes

* Enlarged liver or spleen

* Bone pain

* Headaches

* Confusion or seizures (in severe cases)

Pre-B ALL is most commonly diagnosed in children, but it can also occur in adults. Treatment typically involves a combination of chemotherapy and sometimes bone marrow transplantation. The prognosis for Pre-B ALL is generally good, especially in children, with a high survival rate if treated promptly and effectively. However, the cancer can be more difficult to treat in adults, and the prognosis may be less favorable.

Overall, Pre-B ALL is a rare and aggressive form of leukemia that requires prompt and specialized treatment to improve outcomes for patients.

**Wounds and injuries**refer to any type of damage or harm that occurs to the body as a result of an external force or agent. This can include cuts, lacerations, burns, fractures, sprains, strains, and other types of trauma. Wounds and injuries can be classified as acute or chronic, depending on their duration and severity.

Acute wounds and injuries are those that occur suddenly and heal within a relatively short period of time, usually within a few days or weeks. Examples of acute wounds include cuts, scrapes, and burns. Chronic wounds and injuries, on the other hand, are those that persist over a longer period of time and may not heal properly, leading to long-term complications. Examples of chronic wounds include diabetic foot ulcers, pressure ulcers, and chronic back pain.

Wounds and injuries can be caused by a variety of factors, including accidents, sports injuries, violence, and medical conditions such as diabetes or circulatory problems. Treatment for wounds and injuries depends on the severity of the injury and may include cleaning and dressing the wound, applying antibiotics, immobilizing broken bones, and providing pain management. In some cases, surgery may be necessary to repair damaged tissues or restore function.

Preventive measures for wounds and injuries include wearing appropriate protective gear during activities such as sports or work, following safety protocols to avoid accidents, maintaining proper hygiene and nutrition to prevent infection, and seeking medical attention promptly if an injury occurs.

Overall, wounds and injuries can have a significant impact on an individual's quality of life, and it is important to seek medical attention promptly if symptoms persist or worsen over time. Proper treatment and management of wounds and injuries can help to promote healing, reduce the risk of complications, and improve long-term outcomes.

These disorders are caused by changes in specific genes that fail to function properly, leading to a cascade of effects that can damage cells and tissues throughout the body. Some inherited diseases are the result of single gene mutations, while others are caused by multiple genetic changes.

Inherited diseases can be diagnosed through various methods, including:

1. Genetic testing: This involves analyzing a person's DNA to identify specific genetic changes that may be causing the disease.

2. Blood tests: These can help identify certain inherited diseases by measuring enzyme levels or identifying specific proteins in the blood.

3. Imaging studies: X-rays, CT scans, and MRI scans can help identify structural changes in the body that may be indicative of an inherited disease.

4. Physical examination: A healthcare provider may perform a physical examination to look for signs of an inherited disease, such as unusual physical features or abnormalities.

Inherited diseases can be treated in various ways, depending on the specific condition and its causes. Some treatments include:

1. Medications: These can help manage symptoms and slow the progression of the disease.

2. Surgery: In some cases, surgery may be necessary to correct physical abnormalities or repair damaged tissues.

3. Gene therapy: This involves using genes to treat or prevent inherited diseases.

4. Rehabilitation: Physical therapy, occupational therapy, and other forms of rehabilitation can help individuals with inherited diseases manage their symptoms and improve their quality of life.

Inherited diseases are a significant public health concern, as they affect millions of people worldwide. However, advances in genetic research and medical technology have led to the development of new treatments and management strategies for these conditions. By working with healthcare providers and advocacy groups, individuals with inherited diseases can access the resources and support they need to manage their conditions and improve their quality of life.

**Leukemia**is a cancer that affects the blood and bone marrow, which are responsible for producing blood cells. It occurs when there is an abnormal growth of immature or malignant white blood cells, called leukocytes, in the bone marrow. This can lead to a decrease in the production of healthy red blood cells, platelets, and white blood cells, which can cause a range of symptoms including fatigue, weakness, and increased risk of infection.

There are several different types of leukemia, including:

1. Acute Lymphoblastic Leukemia (ALL): This is the most common type of leukemia in children, but it can also occur in adults. It is characterized by an overproduction of immature white blood cells called lymphoblasts.

2. Acute Myeloid Leukemia (AML): This type of leukemia affects the bone marrow's ability to produce red blood cells, platelets, and other white blood cells. It can occur at any age but is most common in adults.

3. Chronic Lymphocytic Leukemia (CLL): This type of leukemia affects older adults and is characterized by the slow growth of abnormal white blood cells called lymphocytes.

4. Chronic Myeloid Leukemia (CML): This type of leukemia is caused by a genetic mutation in a gene called BCR-ABL. It can occur at any age but is most common in adults.

5. Hairy Cell Leukemia: This is a rare type of leukemia that affects older adults and is characterized by the presence of abnormal white blood cells called hairy cells.

6. Myelodysplastic Syndrome (MDS): This is a group of disorders that occur when the bone marrow is unable to produce healthy blood cells. It can lead to leukemia if left untreated.

Treatment for leukemia depends on the type and severity of the disease, but may include chemotherapy, radiation therapy, targeted therapy, or stem cell transplantation.

**Lung Neoplasms**, also known as lung tumors or pulmonary neoplasms, refer to any abnormal growth of tissue in the lungs that can be benign or malignant. Benign lung neoplasms are non-cancerous and do not spread to other parts of the body, while malignant lung neoplasms are cancerous and have the potential to invade nearby tissues and organs, as well as spread to other parts of the body through the bloodstream or lymphatic system.

There are several types of lung neoplasms, including:

1. Adenocarcinoma: This is the most common type of lung cancer, accounting for approximately 40% of all lung cancers. It is a malignant tumor that originates in the glands of the respiratory tract and can be found in any part of the lung.

2. Squamous cell carcinoma: This type of lung cancer accounts for approximately 25% of all lung cancers and is more common in men than women. It is a malignant tumor that originates in the squamous cells lining the airways of the lungs.

3. Small cell lung cancer (SCLC): This is a highly aggressive form of lung cancer that accounts for approximately 15% of all lung cancers. It is often found in the central parts of the lungs and can spread quickly to other parts of the body.

4. Large cell carcinoma: This is a rare type of lung cancer that accounts for only about 5% of all lung cancers. It is a malignant tumor that originates in the large cells of the respiratory tract and can be found in any part of the lung.

5. Bronchioalveolar carcinoma (BAC): This is a rare type of lung cancer that originates in the cells lining the airways and alveoli of the lungs. It is more common in women than men and tends to affect older individuals.

6. Lymphangioleiomyomatosis (LAM): This is a rare, progressive, and often fatal lung disease that primarily affects women of childbearing age. It is characterized by the growth of smooth muscle-like cells in the lungs and can lead to cysts, lung collapse, and respiratory failure.

7. Hamartoma: This is a benign tumor that originates in the tissue of the lungs and is usually found in children. It is characterized by an overgrowth of normal lung tissue and can be treated with surgery.

8. Secondary lung cancer: This type of cancer occurs when cancer cells from another part of the body spread to the lungs through the bloodstream or lymphatic system. It is more common in people who have a history of smoking or exposure to other carcinogens.

9. Metastatic cancer: This type of cancer occurs when cancer cells from another part of the body spread to the lungs through the bloodstream or lymphatic system. It is more common in people who have a history of smoking or exposure to other carcinogens.

10. Mesothelioma: This is a rare and aggressive form of cancer that originates in the lining of the lungs or abdomen. It is caused by asbestos exposure and can be treated with surgery, chemotherapy, and radiation therapy.

Lung diseases can also be classified based on their cause, such as:

1. Infectious diseases: These are caused by bacteria, viruses, or other microorganisms and can include pneumonia, tuberculosis, and bronchitis.

2. Autoimmune diseases: These are caused by an overactive immune system and can include conditions such as sarcoidosis and idiopathic pulmonary fibrosis.

3. Genetic diseases: These are caused by inherited mutations in genes that affect the lungs and can include cystic fibrosis and primary ciliary dyskinesia.

4. Environmental diseases: These are caused by exposure to harmful substances such as tobacco smoke, air pollution, and asbestos.

5. Radiological diseases: These are caused by exposure to ionizing radiation and can include conditions such as radiographic breast cancer and lung cancer.

6. Vascular diseases: These are caused by problems with the blood vessels in the lungs and can include conditions such as pulmonary embolism and pulmonary hypertension.

7. Tumors: These can be benign or malignant and can include conditions such as lung metastases and lung cancer.

8. Trauma: This can include injuries to the chest or lungs caused by accidents or other forms of trauma.

9. Congenital diseases: These are present at birth and can include conditions such as bronchopulmonary foregut malformations and congenital cystic adenomatoid malformation.

Each type of lung disease has its own set of symptoms, diagnosis, and treatment options. It is important to seek medical attention if you experience any persistent or severe respiratory symptoms, as early diagnosis and treatment can improve outcomes and quality of life.

The term "refractory" refers to the fact that this type of anemia does not respond well to standard treatments, such as blood transfusions or medications. The term "excess blasts" refers to the presence of a large number of immature cells in the bone marrow.

RAEB is a serious and potentially life-threatening condition that can develop into acute myeloid leukemia (AML), a type of cancer that affects the blood and bone marrow. AML is characterized by the rapid growth of abnormal white blood cells, which can crowd out normal cells in the bone marrow and lead to a variety of symptoms, including fatigue, fever, night sweats, and weight loss.

RAEB is usually diagnosed in adults over the age of 60, although it can occur at any age. The condition is often associated with other health problems, such as myelodysplastic syndrome (MDS), a group of disorders that affect the bone marrow and blood cells.

Treatment for RAEB typically involves chemotherapy and/or bone marrow transplantation. The goal of treatment is to slow the progression of the disease, reduce symptoms, and improve quality of life. In some cases, RAEB may be managed with supportive care, such as blood transfusions and antibiotics, to help manage symptoms and prevent complications.

Overall, refractory anemia with excess blasts is a serious and complex condition that requires careful management by a healthcare team of hematologists, oncologists, and other specialists. With appropriate treatment, many people with RAEB are able to achieve long-term remission and improve their quality of life.

**Lymphatic Metastasis**: The spread of cancer cells through the lymphatic system to other parts of the body, such as the liver, lungs, or bones. This type of metastasis is more common in cancers that originate in organs with a high lymphatic drainage, such as breast cancer and melanoma.

Lymphatic metastasis occurs when cancer cells enter the lymphatic vessels and are carried through the lymphatic system to other parts of the body. This can happen through several mechanisms, including:

1. Direct invasion: Cancer cells can invade the nearby lymphatic vessels and spread through them.

2. Lymphatic vessel embolization: Cancer cells can block the flow of lymphatic fluid and cause the formation of a clot-like structure, which can trap cancer cells and allow them to grow.

3. Lymphatic vessel invasion: Cancer cells can infiltrate the walls of lymphatic vessels and spread through them.

Lymphatic metastasis is a common mechanism for the spread of cancer, particularly in the breast, melanoma, and other cancers that have a high risk of lymphatic invasion. The presence of lymphatic metastasis in a patient's body can indicate a more aggressive cancer and a poorer prognosis.

Treatment for lymphatic metastasis typically involves a combination of surgery, chemotherapy, and radiation therapy. Surgery may be used to remove any affected lymph nodes or other tumors that have spread through the lymphatic system. Chemotherapy may be used to kill any remaining cancer cells, while radiation therapy may be used to shrink the tumors and relieve symptoms.

In summary, lymphatic metastasis is a common mechanism for the spread of cancer through the body, particularly in cancers that originate in organs with a high lymphatic drainage. Treatment typically involves a combination of surgery, chemotherapy, and radiation therapy to remove or shrink the tumors and relieve symptoms.

**Postoperative complications**are health problems that occur after surgery, either during the recovery period or weeks or months later. These complications can be related to the surgery itself or to other underlying health issues. Some common postoperative complications include:

1. Infection: Bacterial or viral infections can develop after surgery, potentially leading to sepsis or organ failure.

2. Adhesions: Scar tissue can form during the healing process, which can cause bowel obstruction, chronic pain, or other complications.

3. Wound complications: Incisional hernias, wound dehiscence (separation of the wound edges), and wound infections can occur.

4. Respiratory problems: Pneumonia, respiratory failure, and atelectasis (collapsed lung) can develop after surgery, particularly in older adults or those with pre-existing respiratory conditions.

5. Cardiovascular complications: Myocardial infarction (heart attack), cardiac arrhythmias, and cardiac failure can occur after surgery, especially in high-risk patients.

6. Renal (kidney) problems: Acute kidney injury or chronic kidney disease can develop postoperatively, particularly in patients with pre-existing renal impairment.

7. Neurological complications: Stroke, seizures, and neuropraxia (nerve damage) can occur after surgery, especially in patients with pre-existing neurological conditions.

8. Pulmonary embolism: Blood clots can form in the legs or lungs after surgery, potentially causing pulmonary embolism.

9. Anesthesia-related complications: Respiratory and cardiac complications can occur during anesthesia, including respiratory and cardiac arrest.

10. delayed healing: Wound healing may be delayed or impaired after surgery, particularly in patients with pre-existing medical conditions.

It is important for patients to be aware of these potential complications and to discuss any concerns with their surgeon and healthcare team before undergoing surgery.

**Remission, Spontaneous**: A temporary or permanent reduction or disappearance of symptoms or signs of a disease without any treatment or intervention. This can occur spontaneously or as a result of unknown factors, and it is not necessarily a cure. Remission may be partial or complete, and it does not always indicate the absence of the disease. Spontaneous remission can occur in various conditions, including cancer, autoimmune disorders, and mental health conditions. It is important to note that a spontaneous remission does not necessarily mean that the underlying cause of the disease has been eliminated or cured, and the condition may recur or persist.

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###### Statistical inference2

- I discovered that if I wanted to develop a solid foundation in machine learning then a familiarity with the basics of probability theory and statistical inference would be useful. (goodreads.com)
- This certificate teaches the theory that underpins statistical inference and probability, equipping you to understand the assumptions and limitations of a range of statistical models. (open.ac.uk)

###### Annals of Probability1

- Theodore P. Hill "Partitioning General Probability Measures," The Annals of Probability, Ann. (projecteuclid.org)

###### Conditional probability1

- You will learn what is event, dependent and independent events, simple probability, conditional probability. (math10.com)

###### Mathematics4

- Designed for middle grades mathematics educators that are beginning with or already using TI-Nspireâ„¢ technology and the Building Concepts lesson series, this workshop focuses on strategies for engaging students in new ways of visualizing and thinking about statistics and probability. (ti.com)
- As the authors also emphasise: probability isn't hard mathematics, but what makes it hard is connecting it with the real world and knowing how to apply the vast array of tools available. (goodreads.com)
- Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. (oup.com)
- This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. (oup.com)

###### Bayes2

- Thomas Bayes (1701-1761) ( Figure ) was a Presbyterian Minister, and how he become interested in statistics and probability is uncertain. (cdc.gov)
- Bayes presented his famous theorem on probability in "An Essay Towards Solving a Problem in the Doctrine of Chances," which was published posthumously by his friend Richard Price in 1763. (cdc.gov)

###### Uncertainty4

- Uncertainty is traditionally modelled by a probability distribution, as developed by Kolmogorov , [1] Laplace , de Finetti , [2] Ramsey , Cox , Lindley , and many others. (wikipedia.org)
- Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. (goodreads.com)
- I would like to receive email from MITx and learn about other offerings related to Probability - The Science of Uncertainty and Data. (edx.org)
- Bayesian approaches use prior knowledge and information (e.g., probabilities) that may help reduce uncertainty in analysis and have therefore been increasingly adopted by analysts in public health. (cdc.gov)

###### Theory7

- Imprecise probability generalizes probability theory to allow for partial probability specifications, and is applicable when information is scarce, vague, or conflicting, in which case a unique probability distribution may be hard to identify. (wikipedia.org)
- Walley's theory extends the traditional subjective probability theory via buying and selling prices for gambles, whereas Weichselberger's approach generalizes Kolmogorov 's axioms without imposing an interpretation. (wikipedia.org)
- This book starts from the basic concepts of probability theory and develops it up to the law of large numbers and the central limit theorem (and more). (goodreads.com)
- Study the mathematical theory underlying methods and concepts used in practical statistical analyses while learning to develop probability models and investigate their properties. (open.ac.uk)
- This follows from the fact that probability theory only applies to systems with a finite possibility of occurring at least once in the universe, and it would be inconceivable that 10 158 different trials could ever be made in our entire space-time universe. (icr.org)
- It is a challenging class but will enable you to apply the tools of probability theory to real-world applications or to your research. (edx.org)
- The emphasis of the meeting will be on Algebra, Analysis and Combinatorics as well as the interactions between these areas and probability theory. (euro-math-soc.eu)

###### Theorem1

- Bayes's theorem provides a method of explicitly including prior events or knowledge when considering the probabilities of current events (for example, including a history of smoking when calculating the probability of developing lung cancer). (cdc.gov)

###### Statistics6

- TI-Nspireâ„¢ lessons that support a learning progression for statistics and probability. (ti.com)
- This workshop focuses on strategies for engaging students in new ways of thinking about statistics and probability within and across grades 6, 7 and 8. (ti.com)
- Since machine learning involves a good amount of statistics, I started looking for books or resources on probability. (goodreads.com)
- This statistics illustrates the probability of default (PD) on loans to corporations in Central and Eastern Europe (CEE) as of the first quarter of 2020, by country. (statista.com)
- Be first to hear about new textbooks, new editions, and updates in probability and statistics by ensuring you are correctly signed up to receive e-newsletters from us. (oup.com)
- In general, using statistical weights that reflect the probability of selection and propensity of response for sampled individuals will affect parameter estimates, while incorporating the attributes of the complex sample design (i.e. differential weighting, clustering and stratification) will affect variance estimates (estimated standard errors and thereby test statistics and confidence intervals). (cdc.gov)

###### 20201

- As of the first quarter of 2020, Slovenia displayed the highest probability of a corporate loan defaulting with approximately 4.03 percent. (statista.com)

###### Calculation2

- Determining Lambda for a Poisson probability calculation [Solved! (intmath.com)
- Taken from appropriate cell of life table (as a by-product of life expectancy calculation), i.e. (1-L5 probability to survive by 5)*1000. (who.int)

###### Distributions2

- Standard consistency conditions relate upper and lower probability assignments to non-empty closed convex sets of probability distributions. (wikipedia.org)
- This book teaches basic probability and several of the more common statistical distributions in an academic but easy to read style. (goodreads.com)

###### Theories1

- The first formal treatment dates back at least to the middle of the nineteenth century, by George Boole , [3] who aimed to reconcile the theories of logic and probability. (wikipedia.org)

###### Distribution3

- 5 stars for the effort of giving the intuitive stories for each probability distribution concept. (goodreads.com)
- Consider n variables drawn independently from an arbitrary probability distribution. (brainmass.com)
- We introduce the Precipitation Probability DISTribution (PPDIST) dataset, a collection of global high-resolution (0.1Â°) observation-based climatologies (1979-2018) of the occurrence and peak intensity of precipitation ( P ) at daily and 3-hourly time-scales. (nature.com)

###### Interval3

- People have a limited ability to determine their own subjective probabilities and might find that they can only provide an interval. (wikipedia.org)
- Perhaps the most common generalization is to replace a single probability specification with an interval specification. (wikipedia.org)
- In the 1920s, in A Treatise on Probability , Keynes [11] formulated and applied an explicit interval estimate approach to probability. (wikipedia.org)

###### Introduction1

- The contents of this courseare heavily based upon the corresponding MIT class -- Introduction to Probability -- a course that has been offered and continuously refined over more than 50 years. (edx.org)

###### YEARS2

- For several years, physicians have determined that the use of selective serotonin reuptake inhibitors (SSRIs) may influence the probability of a stroke on depressed people. (articlealley.com)
- Under the terms of the deal, Probability will create several exciting slot games based on famous movies produced by Paramount over the years. (bonusgambling.org)

###### Widely1

- Single Sheet Inkjet Tattoo Transfer Paper In all probability probably the most well known and most widely out there kind of tattoo paper may be the single sheet assortment. (articlealley.com)

###### Find1

- However, how do i find the probabilities? (physicsforums.com)

###### Page2

- See our page on Calculating the Probability of Causation for more information. (cdc.gov)
- dmf: I suspect calculating the final probabilities would be quite involved, as the page you linked to indicates. (intmath.com)

###### Models1

- Work on imprecise probability models proceeded fitfully throughout the 20th century, with important contributions by Bernard Koopman , C.A.B. Smith , I.J. Good , Arthur Dempster , Glenn Shafer , Peter M. Williams , Henry Kyburg , Isaac Levi , and Teddy Seidenfeld . (wikipedia.org)

###### Identify1

- Identify several (e.g., five to seven) high-probability requests-those that the student follows 80% to 100% of the time-that relate to the context of the low-p request. (vanderbilt.edu)

###### Results2

- 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)
- This report presents results of an investigation into the influence of disk electrode material on the probability of. (cdc.gov)

###### Influence1

- The Bureau of Mines completed an investigation of the influence of material on the ignition probability using the breakflash apparatus. (cdc.gov)

###### Complex2

- Now, maybe Durangobill would be able to tie all this into the already complex probability calculations for 7-card hands! (intmath.com)
- As stated in the module on sampling in NHANES, the NHANES has a complex, multistage, probability cluster design. (cdc.gov)

###### General1

- We derive the general expression of the probability density for the kth largest variable. (brainmass.com)

###### Give1

- And then the coefficients squared give me the probabilities of measuring each eigenvalue as a function of time. (physicsforums.com)

###### Idea2

- The idea to use imprecise probability has a long history. (wikipedia.org)
- That is the idea that probabilities don't add they multiply. (medscape.com)

###### Default2

- Estonia on the other hand during the same period had a probability of default (PD) rate of almost one percent. (statista.com)
- The BBVA categorize probability of default as "a measure of credit rating that is assigned internally to a customer or a contract with the aim of estimating the probability of non-compliance within a year. (statista.com)

###### Function1

- A lower probability function is superadditive but not necessarily additive, whereas an upper probability is subadditive. (wikipedia.org)

###### Life2

- It does not just introduce the concept but provides many examples of applying probability in real-life situations. (goodreads.com)
- Life is a school of probability. (causeweb.org)

###### Book1

- [12] At the start of the 1990s, the field started to gather some momentum, with the publication of Peter Walley 's book Statistical Reasoning with Imprecise Probabilities [7] (which is also where the term "imprecise probability" originates). (wikipedia.org)

###### Figure1

- Import products to Magento, an easy way If you are browsing this write-up you are in all probability attempting to figure out how you can import your files to Magento. (articlealley.com)