The Annals of Applied Probability

Adaptive Gibbs samplers and related MCMC methods

Krzysztof Łatuszyński, Gareth O. Roberts, and Jeffrey S. Rosenthal

Full-text: Open access

Abstract

We consider various versions of adaptive Gibbs and Metropolis-within-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run by learning as they go in an attempt to optimize the algorithm. We present a cautionary example of how even a simple-seeming adaptive Gibbs sampler may fail to converge. We then present various positive results guaranteeing convergence of adaptive Gibbs samplers under certain conditions.

Article information

Source
Ann. Appl. Probab. Volume 23, Number 1 (2013), 66-98.

Dates
First available in Project Euclid: 25 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1359124382

Digital Object Identifier
doi:10.1214/11-AAP806

Mathematical Reviews number (MathSciNet)
MR3059204

Zentralblatt MATH identifier
1263.60067

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces 65C05: Monte Carlo methods
Secondary: 62F15: Bayesian inference

Keywords
MCMC estimation adaptive MCMC Gibbs sampling

Citation

Łatuszyński, Krzysztof; Roberts, Gareth O.; Rosenthal, Jeffrey S. Adaptive Gibbs samplers and related MCMC methods. Ann. Appl. Probab. 23 (2013), no. 1, 66--98. doi:10.1214/11-AAP806. https://projecteuclid.org/euclid.aoap/1359124382


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