Bayesian inference using Gibbs sampling

{{Short description|Statistical software for Bayesian inference}}

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Bayesian inference using Gibbs sampling (BUGS) is a statistical software for performing Bayesian inference using Markov chain Monte Carlo (MCMC) methods. It was developed by David Spiegelhalter at the Medical Research Council Biostatistics Unit in Cambridge in 1989 and released as free software in 1991.{{Cite journal |last1=Lunn |first1=David |last2=Spiegelhalter |first2=David |last3=Thomas |first3=Andrew |last4=Best |first4=Nicky |date=2009 |title=The BUGS project: Evolution, critique and future directions |journal=Statistics in Medicine |language=en |volume=28 |issue=25 |pages=3049–3067 |doi=10.1002/sim.3680 |pmid=19630097 |doi-access=free}} {{Cite book |last=McGrayne |first=Sharon Bertsch |title=The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries |publisher=Yale University Press |year=2012 |isbn=9780300188226 |pages=226 |language=en}}

The BUGS project has evolved through four main versions: ClassicBUGS,{{Cite journal |last1=Gilks |first1=W. R. |last2=Thomas |first2=A. |last3=Spiegelhalter |first3=D. J. |date=1994 |title=A Language and Program for Complex Bayesian Modelling |url=https://rss.onlinelibrary.wiley.com/doi/abs/10.2307/2348941 |journal=The Statistician |volume=43 |issue=1 |pages=169–177 |doi=10.2307/2348941|jstor=2348941 }} WinBUGS,{{Cite journal |last1=Lunn |first1=David J. |last2=Thomas |first2=Andrew |last3=Best |first3=Nicky |last4=Spiegelhalter |first4=David |date=2000 |title=WinBUGS—A Bayesian modelling framework: concepts, structure, and extensibility |url=http://link.springer.com/10.1023/A:1008929526011 |journal=Statistics and Computing |volume=10 |issue=4 |pages=325–337 |doi=10.1023/A:1008929526011|s2cid=2722195 }} OpenBUGS and [https://www.multibugs.org/ MultiBUGS].{{Cite journal |last1=Goudie |first1=Robert J. B. |last2=Turner |first2=Rebecca M. |last3=De Angelis |first3=Daniela |last4=Thomas |first4=Andrew |date=2020 |title=MultiBUGS: A Parallel Implementation of the BUGS Modeling Framework for Faster Bayesian Inference |journal=Journal of Statistical Software |language=en |volume=95 |issue=7 |pages=1–20 |doi=10.18637/jss.v095.i07 |pmid=33071678 |pmc=7116196 |doi-access=free}} MultiBUGS is built on the existing algorithms and tools in OpenBUGS and WinBUGS, which are no longer developed, and implements parallelization to speed up computation. Several R packages are available, [https://github.com/MultiBUGS/R2MultiBUGS R2MultiBUGS] acts as an interface to MultiBUGS, while [https://r-nimble.org/ Nimble] is an extension of the BUGS language.

Alternative implementations of the BUGS language include JAGS and Stan.