Markov chain Monte Carlo (MCMC) is the engine of modern Bayesian statistics, being used to approximate the posterior and derived quantities of interest. Despite this, the issue of how the output from a Markov chain is post-processed and reported is often overlooked. Convergence diagnostics can be used to control bias via burn-in removal, but these do not account for (common) situations where a limited computational budget engenders a bias-variance trade-off. The aim of this article is to review state-of-the-art techniques for post-processing Markov chain output. Our review covers methods based on discrepancy minimisation, which directly address the bias-variance trade-off, as well as general-purpose control variate methods for approximating expected quantities of interest.

翻译：Markov链条Monte Carlo(MCMC)是现代Bayesian统计数据的引擎,用于近似后端和衍生利益量,尽管如此,Markov链条的输出如何经过处理和报告往往被忽略了。聚合诊断可用于通过燃烧去除来控制偏差,但这并不包括(常见)有限计算预算造成偏差权衡的情况。本条款的目的是审查后处理Markov链条输出的最新技术。我们的审查涵盖了基于差异最小化的方法,直接解决偏差偏差权衡,以及通用控制变量法,以接近预期利息量。