Bayesian parameter estimation for latent Markov random fields and social networks

Everitt, R. G. (2012) Bayesian parameter estimation for latent Markov random fields and social networks. Journal of Computational and Graphical Statistics, 21 (4). pp. 940-960. ISSN 1061-8600 doi: 10.1080/10618600.2012.687493

Abstract/Summary

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.

Additional Information	This article is available on the publisher website at http://www.tandfonline.com/doi/full/10.1080/10618600.2012.687493
Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/29117
Identification Number/DOI	10.1080/10618600.2012.687493
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics > Applied Statistics
Uncontrolled Keywords	approximate bayesian computation,carlo,exponential random graphs,graphical models,intractable normalising constants,particle markov chain monte
Additional Information	This article is available on the publisher website at http://www.tandfonline.com/doi/full/10.1080/10618600.2012.687493
Publisher	American Statistical Association
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