Variational Bayes for estimating the parameters of a hidden Potts model

McGrory, C. A., Titterington, D. M., Reeves, R. and Pettitt, A. N. (2009) Variational Bayes for estimating the parameters of a hidden Potts model. Statistics and Computing, 19 3: 329-340. doi:10.1007/s11222-008-9095-6

Author McGrory, C. A.
Titterington, D. M.
Reeves, R.
Pettitt, A. N.
Title Variational Bayes for estimating the parameters of a hidden Potts model
Journal name Statistics and Computing   Check publisher's open access policy
ISSN 0960-3174
Publication date 2009-09
Sub-type Article (original research)
DOI 10.1007/s11222-008-9095-6
Volume 19
Issue 3
Start page 329
End page 340
Total pages 12
Place of publication Secaucus, NJ, United States
Publisher Springer New York LLC
Language eng
Abstract Hidden Markov random field models provide an appealing representation of images and other spatial problems. The drawback is that inference is not straightforward for these models as the normalisation constant for the likelihood is generally intractable except for very small observation sets. Variational methods are an emerging tool for Bayesian inference and they have already been successfully applied in other contexts. Focusing on the particular case of a hidden Potts model with Gaussian noise, we show how variational Bayesian methods can be applied to hidden Markov random field inference. To tackle the obstacle of the intractable normalising constant for the likelihood, we explore alternative estimation approaches for incorporation into the variational Bayes algorithm. We consider a pseudo-likelihood approach as well as the more recent reduced dependence approximation of the normalisation constant. To illustrate the effectiveness of these approaches we present empirical results from the analysis of simulated datasets. We also analyse a real dataset and compare results with those of previous analyses as well as those obtained from the recently developed auxiliary variable MCMC method and the recursive MCMC method. Our results show that the variational Bayesian analyses can be carried out much faster than the MCMC analyses and produce good estimates of model parameters. We also found that the reduced dependence approximation of the normalisation constant outperformed the pseudo-likelihood approximation in our analysis of real and synthetic datasets.
Keyword Potts/Ising model
Hidden Markov random field
Variational approximation
Bayesian inference
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Created: Tue, 24 Jan 2012, 13:44:45 EST by Kay Mackie on behalf of School of Mathematics & Physics