Convergence of Markov Chain Monte Carlo Algorithms¹

作者：Nicholas G. Polson · 年份：1996 · DOI：10.1093/oso/9780198523567.003.0016 · 被引用次数：29 · 研究领域：Markov Chains and Monte Carlo Methods、Bayesian Methods and Mixture Models、Statistical Methods and Inference

Abstract This paper explores convergence properties of Markov chain Monte Carlo algorithms. These algorithms provide a simulation based strategy for sampling from high dimensional probability distributions. We describe techniques for analysing the convergence rate of the chain and show how this determines the running time of an algorithm. For log-concave distributions, a polynomial time running time bound of Frieze, Kannan and Polson (1993) for a local Metropolis algorithm is discussed. The running time depends on dimension, local curvature, sampling accuracy and starting distribution. For several examples, we illustrate how dimension and correlation structure affect the running time. For non-log-concave distributions, we propose the use of latent variables to speed up convergence. Implementation issues are described and limitations of relying on limit theorems to assess convergence are discussed. An analysis of the mean squared error of a delayed average estimator is given.