Software tools for Bayesian inference have undergone rapid evolution in the past three decades, following popularisation of the first generation MCMC-sampler implementations. More recently, exponential growth in the number of users has been stimulated both by the active development of new packages by the machine learning community and popularity of specialist software for particular applications. This review aims to summarize the most popular software and provide a useful map for a reader to navigate the world of Bayesian computation. We anticipate a vigorous continued development of algorithms and corresponding software in multiple research fields, such as probabilistic programming, likelihood-free inference, and Bayesian neural networks, which will further broaden the possibilities for employing the Bayesian paradigm in exciting applications.
Erik Štrumbelj’s work is partially funded by the Slovenian Research Agency (research core funding No. P2- 0442). Andrew Gelman’s work is partially funded by the U.S. Office of Naval Research. Special thanks to Christian Robert for the initiative and encouragement for this work.