Quantifying uncertainty in transdimensional Markov chain Monte Carlo using discrete Markov models

Heck, Daniel W. ; Overstall, Antony M. ; Gronau, Quentin F. ; Wagenmakers, Eric-Jan

DOI: https://doi.org/10.1007/s11222-018-9828-0
URL: https://link.springer.com/article/10.1007/s11222-0...
Additional URL: https://arxiv.org/abs/1703.10364
Document Type: Article
Year of publication: 2019
The title of a journal, publication series: Statistics and Computing : SC
Volume: 29
Issue number: 4
Page range: 631-643
Place of publication: Dordrecht [u.a.]
Publishing house: Springer Science + Business Media
ISSN: 0960-3174 , 1573-1375
Related URLs:
Publication language: English
Institution: School of Social Sciences > Kognitive Psychologie u. Differentielle Psychologie (Erdfelder)
Außerfakultäre Einrichtungen > Graduate School of Economic and Social Sciences- CDSS (Social Sciences)
Subject: 150 Psychology
Keywords (English): Reversible jump MCMC , Product space MCMC , Bayesian model selection , Posterior model probabilities , Bayes factor
Abstract: Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC) relies on sampling a discrete indexing variable to estimate the posterior model probabilities. However, little attention has been paid to the precision of these estimates. If only few switches occur between the models in the transdimensional MCMC output, precision may be low and assessment based on the assumption of independent samples misleading. Here, we propose a new method to estimate the precision based on the observed transition matrix of the model-indexing variable. Assuming a first-order Markov model, the method samples from the posterior of the stationary distribution. This allows assessment of the uncertainty in the estimated posterior model probabilities, model ranks, and Bayes factors. Moreover, the method provides an estimate for the effective sample size of the MCMC output. In two model selection examples, we show that the proposed approach provides a good assessment of the uncertainty associated with the estimated posterior model probabilities.

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