Convergence rates of Metropolis–Hastings algorithms.

Given a target probability density known up to a normalizing constant, the Metropolis–Hastings algorithm simulates realizations from a Markov chain which are eventual realizations from the target probability density. A key element for ensuring a reliable Metropolis–Hastings simulation experiment is understanding how quickly the simulation will generate a representative sample from target density. This corresponds to understanding the convergence properties of the Metropolis–Hastings Markov chain. State‐of‐the‐art methods for convergence analysis of Metropolis–Hastings algorithms are considered and reviewed. Practically important topics are discussed for an interdisciplinary audience. This includes convergence properties in high dimensions, proper tuning, initialization, and limitations of current convergence analyses. This article is categorized under:Statistical and Graphical Methods of Data Analysis > Markov Chain Monte CarloStatistical and Graphical Methods of Data Analysis > Monte Carlo MethodsStatistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory [ABSTRACT FROM AUTHOR]