QUT ePrints

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.

View at publisher

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.

Impact and interest:

12 citations in Scopus
Search Google Scholar™
14 citations in Web of Science®

Citation countsare sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

Full-text downloads:

344 since deposited on 15 Sep 2008
165 in the past twelve months

Full-text downloadsdisplays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.

ID Code: 14859
Item Type: Journal Article
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 http://www.springerlink.com
Deposited On: 15 Sep 2008
Last Modified: 29 Feb 2012 23:43

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page