Transitional Markov Chain Monte Carlo: Observations and Improvements
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VIEW THE REPLYPublication: Journal of Engineering Mechanics
Volume 142, Issue 5
Abstract
The Transitional Markov chain Monte Carlo (TMCMC) method is a widely used method for Bayesian updating and Bayesian model class selection. The method is based on successively sampling from a sequence of distributions that gradually approach the posterior target distribution. The samples of the intermediate distributions are used to obtain an estimate of the evidence, which is needed in the context of Bayesian model class selection. The properties of the TMCMC method are discussed and the following three modifications to the TMCMC method are proposed: (1) The sample weights should be adjusted after each MCMC step; (2) a burn-in period in the MCMC sampling step can improve the posterior approximation; and (3) the scale of the proposal distribution of the MCMC algorithm can be selected adaptively to achieve a near-optimal acceptance rate. The performance of the proposed modifications is compared with the original TMCMC method by means of three example problems. The proposed modifications reduce the bias in the estimate of the evidence, and improve the convergence behavior of posterior estimates.
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Published In
Journal of Engineering Mechanics
Volume 142 • Issue 5 • May 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: May 13, 2015
Accepted: Dec 3, 2015
Published online: Feb 1, 2016
Published in print: May 1, 2016
Discussion open until: Jul 1, 2016
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