Fixed-width output analysis for Markov chain Monte Carlo

2006/01/18 by Galin Jones, Galin L. Jones, Jones, Galin +7 · 1 citation
Computer Science · Mathematics · #65C40 #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:65C40 #stat.TH

paper · pdf · doi:10.48550/arxiv.math/0601446

arxiv created 2006/01/18 · openalex publication_date 2006/01/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a target distribution via ergodic averages. A fundamental question is when should sampling stop? That is, when are the ergodic averages good estimates of the desired quantities? We consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user-specified value. Hence calculating a Monte Carlo standard error is a critical step in assessing the simulation output. We consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution. We give sufficient conditions for the strong consistency of both methods and investigate their finite sample properties in a variety of examples.

Citations

• Algebraic algorithms for sampling from conditional distributions
• The Asymptotic Validity of Sequential Stopping Rules for Stochastic Simulations
• On the Markov chain central limit theorem

Cited by

• Convergence monitoring of quantum Gibbs samplers
• Double Machine Learning for Causal Inference under Shared-State Interference

Related

• Multivariate Output Analysis for Markov chain Monte Carlo
• Regeneration and Fixed-Width Analysis of Markov Chain Monte Carlo Algorithms
• Relative fixed-width stopping rules for Markov chain Monte Carlo simulations
• Analyzing MCMC Output
• Principle of detailed balance and convergence assessment of Markov Chain Monte Carlo methods and simulated annealing