A Bayesian network is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one of several forms of causal notation, causal networks are special cases of Bayesian networks. Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases.
In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by recording states from the chain. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Various algorithms exist for constructing chains, including the Metropolis–Hastings algorithm.
Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a degree of belief in an event. The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event. This differs from a number of other interpretations of probability, such as the frequentist interpretation that views probability as the limit of the relative frequency of an event after many trials.
A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics—particularly Bayesian statistics—and machine learning.
Alexander Philip Dawid is Emeritus Professor of Statistics of the University of Cambridge, and a Fellow of Darwin College, Cambridge. He is a leading proponent of Bayesian statistics.
Sir David John Spiegelhalter is a British statistician and a Fellow of Churchill College, Cambridge. From 2007 to 2018 he was Winton Professor of the Public Understanding of Risk in the Statistical Laboratory at the University of Cambridge. Spiegelhalter is an ISI highly cited researcher.
OpenBUGS is a software application for the Bayesian analysis of complex statistical models using Markov chain Monte Carlo (MCMC) methods. OpenBUGS is the open source variant of WinBUGS. It runs under Microsoft Windows and Linux, as well as from inside the R statistical package. Versions from v3.0.7 onwards have been designed to be at least as efficient and reliable as WinBUGS over a range of test applications.
Bayesian inference of phylogeny combines the information in the prior and in the data likelihood to create the so-called posterior probability of trees, which is the probability that the tree is correct given the data, the prior and the likelihood model. Bayesian inference was introduced into molecular phylogenetics in the 1990s by three independent groups: Bruce Rannala and Ziheng Yang in Berkeley, Bob Mau in Madison, and Shuying Li in University of Iowa, the last two being PhD students at the time. The approach has become very popular since the release of the MrBayes software in 2001, and is now one of the most popular methods in molecular phylogenetics.
WinBUGS is statistical software for Bayesian analysis using Markov chain Monte Carlo (MCMC) methods.
GNU MCSim is a suite of simulation software. It allows one to design one's own statistical or simulation models, perform Monte Carlo simulations, and Bayesian inference through (tempered) Markov chain Monte Carlo simulations. The latest version allows parallel computing of Monte Carlo or MCMC simulations.
Just another Gibbs sampler (JAGS) is a program for simulation from Bayesian hierarchical models using Markov chain Monte Carlo (MCMC), developed by Martyn Plummer. JAGS has been employed for statistical work in many fields, for example ecology, management, and genetics.
Probabilistic programming (PP) is a programming paradigm in which probabilistic models are specified and inference for these models is performed automatically. It represents an attempt to unify probabilistic modeling and traditional general purpose programming in order to make the former easier and more widely applicable. It can be used to create systems that help make decisions in the face of uncertainty.
Stan is a probabilistic programming language for statistical inference written in C++. The Stan language is used to specify a (Bayesian) statistical model with an imperative program calculating the log probability density function.
JASP is a free and open-source program for statistical analysis supported by the University of Amsterdam. It is designed to be easy to use, and familiar to users of SPSS. It offers standard analysis procedures in both their classical and Bayesian form. JASP generally produces APA style results tables and plots to ease publication. It promotes open science via integration with the Open Science Framework and reproducibility by integrating the analysis settings into the results. The development of JASP is financially supported by several universities and research funds. As the JASP GUI is developed in C++ using Qt framework, some of the team left to make a notable fork which is Jamovi which has its GUI developed in JavaScript and HTML5.
Sudipto Banerjee is an Indian-American statistician best known for his work on Bayesian hierarchical modeling and inference for spatial data analysis. He is Professor of Biostatistics and Senior Associate Dean in the School of Public Health at the University of California, Los Angeles. He served as the Chair of the Department of Biostatistics at UCLA from 2014 through 2023. He also served as the 2022 President of the International Society for Bayesian Analysis.
PyMC is a probabilistic programming language written in Python. It can be used for Bayesian statistical modeling and probabilistic machine learning.
Nicola G. "Nicky" Best is a statistician known for her work on the deviance information criterion in Bayesian inference[B][E] and as a developer of Bayesian inference using Gibbs sampling.[A][D] She is a former professor of biostatistics and epidemiology at Imperial College London and is currently a biostatistician for GlaxoSmithKline.
ArviZ is a Python package for exploratory analysis of Bayesian models.
In Bayesian statistics, the Probability of Direction (pd) is a measure of effect existence representing the certainty with which an effect is positive or negative. This index is numerically similar to the frequentist p-value.
