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Annual Review of Statistics and Its Application

Volume 10, 2023

Simulation-Based Bayesian Analysis

Abstract

I consider the development of Markov chain Monte Carlo (MCMC) methods, from late-1980s Gibbs sampling to present-day gradient-based methods and piecewise-deterministic Markov processes. In parallel, I show how these ideas have been implemented in successive generations of statistical software for Bayesian inference. These software packages have been instrumental in popularizing applied Bayesian modeling across a wide variety of scientific domains. They provide an invaluable service to applied statisticians in hiding the complexities of MCMC from the user while providing a convenient modeling language and tools to summarize the output from a Bayesian model. As research into new MCMC methods remains very active, it is likely that future generations of software will incorporate new methods to improve the user experience.

Keyword(s): Bayesian computation, Bayesian inference, BUGS, Gibbs sampling, graphical model, INLA, JAGS, MCMC, PDMPs, Stan, statistical software
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2023-03-09
2024-04-30
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/content/journals/10.1146/annurev-statistics-122121-040905
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Simulation-Based Bayesian Analysis
Annual Review of Statistics and Its Application 10, 401 (2023); https://doi.org/10.1146/annurev-statistics-122121-040905
/content/journals/10.1146/annurev-statistics-122121-040905
/content/journals/10.1146/annurev-statistics-122121-040905
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