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.

中文翻译：

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基于模拟的贝叶斯分析


我考虑了马尔可夫链蒙特卡罗 (MCMC) 方法的发展，从 20 世纪 80 年代末的吉布斯采样到当今基于梯度的方法和分段确定性马尔可夫过程。同时，我展示了如何在连续几代贝叶斯推理统计软件中实现这些想法。这些软件包对于在各个科学领域推广应用贝叶斯建模发挥了重要作用。它们为应用统计学家提供了宝贵的服务，向用户隐藏 MCMC 的复杂性，同时提供方便的建模语言和工具来总结贝叶斯模型的输出。由于对新 MCMC 方法的研究仍然非常活跃，未来几代软件很可能会采用新方法来改善用户体验。