A Short Review of Ergodicity and Convergence of Markov chain Monte Carlo Estimators
Michael Betancourt
TL;DR
This paper reviews the fundamental theories behind the convergence properties of Markov chain Monte Carlo estimators, focusing on both their long-term and short-term behaviors.
Contribution
It provides a concise overview of the existing theoretical framework for analyzing MCMC estimator convergence, highlighting key concepts and recent developments.
Findings
Summarizes core ergodicity concepts for MCMC
Discusses convergence rate bounds and criteria
Highlights recent advances in theoretical understanding
Abstract
This short note reviews the basic theory for quantifying both the asymptotic and preasymptotic convergence of Markov chain Monte Carlo estimators.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Statistical Methods and Inference · Stochastic processes and statistical mechanics