A recursive algorithm for Markov random fields

Authors: Bartolucci F.¹; Besag J.²

Source: Biometrika, Volume 89, Number 3, August 2002 , pp. 724-730(7)

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Abstract:

We propose a recursive algorithm as a more useful alternative to the Brook expansion for the joint distribution of a vector of random variables when the original formulation is in terms of the corresponding full conditional distributions, as occurs for Markov random fields. Usually, in practical applications, the computational load will still be excessive but then the algorithm can be used to obtain the componentwise full conditionals of a system after marginalising over some variables or the joint distribution of subsets of the variables, conditioned on values of the remainder, which is required for block Gibbs sampling. As an illustrative example, we apply the algorithm in the simplest nontrivial setting of hidden Markov chains. More important, we demonstrate how it applies to Markov random fields on regular lattices and to perfect block Gibbs sampling for binary systems.

Keywords: Autologistic distribution; Binary system; Full conditional; Graphical model; Hidden Markov chain; Markov chain Monte Carlo; Markov random field; Monotone coupling from the past

Document Type: Research article

DOI: http://dx.doi.org/10.1093/biomet/89.3.724

Affiliations: 1: Department of Statistics, Box 1315, University of Perugia, Perugia 06100, Italy, Email: bart@stat.unipg.it 2: Department of Statistics, Box 354322, University of Washington, Seattle, Washington 98195, U.S.A., Email: julian@stat.washington.edu

Publication date: 2002-08-01