Variational Bayes for estimating the parameters of a hidden Potts model

McGrory, Clare A., Titterington, D. M., Reeves, Robert W., & Pettitt, Anthony N. (2008) Variational Bayes for estimating the parameters of a hidden Potts model. Statistics and Computing, In Press.

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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.

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24 citations in Scopus
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27 citations in Web of Science®

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ID Code: 14859
Item Type: Journal Article
Refereed: Yes
Keywords: Potts/Ising model, Hidden Markov random field, Variational approximation, Bayesian inference, Pseudo, likelihood, Reduced dependence approximation
DOI: 10.1007/s11222-008-9095-6
ISSN: 1573-1375
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright Springer
Copyright Statement: The original publication is available at SpringerLink
Deposited On: 15 Sep 2008 00:00
Last Modified: 29 Feb 2012 13:43

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