Quantifying uncertainty in transdimensional Markov chain Monte Carlo using discrete Markov models
Quantifying uncertainty in transdimensional Markov chain Monte Carlo using discrete Markov models
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.
631-643
Heck, Daniel
96504b3b-1726-460d-818a-94e49ff50b5c
Overstall, Antony
c1d6c8bd-1c5f-49ee-a845-ec9ec7b20910
Gronau, Quentin
95d1ec22-811a-4523-a2af-f07e31bbac83
Wagenmakers, Eric-Jan
122aedf6-9c4b-49aa-9a08-00e0d1c47880
Heck, Daniel
96504b3b-1726-460d-818a-94e49ff50b5c
Overstall, Antony
c1d6c8bd-1c5f-49ee-a845-ec9ec7b20910
Gronau, Quentin
95d1ec22-811a-4523-a2af-f07e31bbac83
Wagenmakers, Eric-Jan
122aedf6-9c4b-49aa-9a08-00e0d1c47880
Heck, Daniel, Overstall, Antony, Gronau, Quentin and Wagenmakers, Eric-Jan
(2018)
Quantifying uncertainty in transdimensional Markov chain Monte Carlo using discrete Markov models.
Statistics and Computing, 29 (4), .
(doi:10.1007/s11222-018-9828-0).
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.
Text
Quantifying Uncertainty
- Version of Record
More information
Accepted/In Press date: 2 August 2018
e-pub ahead of print date: 9 August 2018
Identifiers
Local EPrints ID: 423109
URI: http://eprints.soton.ac.uk/id/eprint/423109
ISSN: 0960-3174
PURE UUID: 331a8a9f-da82-4844-b1c0-11cd01b7f3b1
Catalogue record
Date deposited: 14 Aug 2018 16:30
Last modified: 16 Mar 2024 03:53
Export record
Altmetrics
Contributors
Author:
Daniel Heck
Author:
Quentin Gronau
Author:
Eric-Jan Wagenmakers
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics