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Related Concept Videos

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
Probability Distributions01:32

Probability Distributions

The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
Binomial Probability Distribution01:15

Binomial Probability Distribution

A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
Poisson Probability Distribution01:09

Poisson Probability Distribution

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
Probability Histograms01:17

Probability Histograms

A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.

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Related Experiment Video

Updated: May 25, 2026

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
12:39

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types

Published on: December 10, 2012

Bayesian posterior distributions without Markov chains.

Stephen R Cole1, Haitao Chu, Sander Greenland

  • 1Department of Epidemiology, Gillings School of Global Public Health, University of North Carolina at Chapel Hill, 27599-7435, USA. cole@unc.edu

American Journal of Epidemiology
|February 7, 2012
PubMed
Summary

Rejection sampling offers a transparent alternative to Markov chain Monte Carlo (MCMC) for Bayesian inference. This method aids understanding and yields comparable results in complex studies, though with longer run times.

Related Experiment Videos

Last Updated: May 25, 2026

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
12:39

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types

Published on: December 10, 2012

Area of Science:

  • Biostatistics
  • Computational Statistics
  • Epidemiology

Background:

  • Bayesian inference often relies on Markov chain Monte Carlo (MCMC) for simulating posterior distributions.
  • MCMC methods can be complex and pose a barrier to understanding Bayesian inference for novices.

Purpose of the Study:

  • To introduce and illustrate a transparent rejection sampling method as an accessible alternative to MCMC for Bayesian inference.
  • To demonstrate the feasibility and accuracy of rejection sampling in two distinct epidemiological studies.

Main Methods:

  • Rejection sampling was applied to a case-control study on magnetic fields and childhood cancer.
  • Rejection sampling was also applied to a cohort study on HIV viral load and AIDS incidence.
  • Results were compared with MCMC and data-augmentation prior methods.

Main Results:

  • In both examples, rejection sampling produced results similar to MCMC and other approximation methods.
  • The case-control study yielded an odds ratio (OR) of 1.69 (95% PI: 0.57, 5.00) via rejection sampling.
  • The HIV cohort study, while feasible, showed longer run times for rejection sampling compared to MCMC.

Conclusions:

  • Rejection sampling provides a transparent and understandable approach to Bayesian inference.
  • The method is a viable alternative to MCMC, particularly for educational purposes, despite potential increases in computation time.
  • While less broadly applicable than MCMC, rejection sampling offers valuable insights into Bayesian analysis.