Convergence Diagnostics for Markov Chain Monte Carlo

2019/11/20 by Vivekananda Roy · 1 voice · 1 citation
Mathematics · Computer Science · #Markov Chains and Monte Carlo Methods #Bayesian Methods and Mixture Models #Statistical Methods and Inference

paper · pdf · doi:10.1146/annurev-statistics-031219-041300

openalex publication_date 2019/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Markov chain Monte Carlo (MCMC) is one of the most useful approaches to scientific computing because of its flexible construction, ease of use, and generality. Indeed, MCMC is indispensable for performing Bayesian analysis. Two critical questions that MCMC practitioners need to address are where to start and when to stop the simulation. Although a great amount of research has gone into establishing convergence criteria and stopping rules with sound theoretical foundation, in practice, MCMC users often decide convergence by applying empirical diagnostic tools. This review article discusses the most widely used MCMC convergence diagnostic tools. Some recently proposed stopping rules with firm theoretical footing are also presented. The convergence diagnostics and stopping rules are illustrated using three detailed examples.

Citations

• The Asymptotic Validity of Sequential Stopping Rules for Stochastic Simulations
• Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables
• Renewal theory and computable convergence rates for geometrically ergodic Markov chains
• Inference from Iterative Simulation Using Multiple Sequences

Cited by

• Self-Tuned Rejection Sampling within Gibbs and a Case Study in Small Area Estimation

Discussions

• @risi.bsky.social This review of #MCMC convergence diagnostics is VERY good www.annualreviews.org/content/jour... It pairs well with this article about convergence of #MonteCarlo in #GPU friendly s [bsky, 1 points, 0 comments]

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