Fixed-Width Output Analysis for Markov Chain Monte Carlo

Markov chain Monte Carlo is a method of producing a correlated sample to estimate features of a target distribution through ergodic averages. A fundamental question is when sampling should stop; that is, at what point the ergodic averages are good estimates of the desired quantities. We consider a m...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2006-12, Vol.101 (476), p.1537-1547
Main Authors: Jones, Galin L, Haran, Murali, Caffo, Brian S, Neath, Ronald
Format: Article
Language:English
Subjects:
Applications
Arithmetic mean
Batch means
Confidence interval
Distribution
Ergodic theory
Error
Estimation
Estimation methods
Estimators
Exact sciences and technology
General topics
Geometric ergodicity
Markov analysis
Markov chain
Markov chains
Markov processes
Markovian processes
Mathematics
Metropolitan areas
Monte Carlo central limit theorem
Monte Carlo simulation
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
P values
Probabilities
Probability and statistics
Probability theory and stochastic processes
Regeneration
Research methodology
Sampling
Sampling techniques
Sciences and techniques of general use
Simulation
Statistical methods
Statistical variance
Statistics
Theory and Methods
Variance
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Description
Summary:Markov chain Monte Carlo is a method of producing a correlated sample to estimate features of a target distribution through ergodic averages. A fundamental question is when sampling should stop; that is, at what point the ergodic averages are 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 various examples.
ISSN:0162-1459
1537-274X
DOI:10.1198/016214506000000492