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Biometrika Advance Access originally published online on August 5, 2007
Biometrika 2007 94(3):661-672; doi:10.1093/biomet/asm052
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Copyright © 2007 Biometrika Trust

Articles

Recursive computing and simulation-free inference for general factorizable models

Nial Friel

Department of Statistics, University of Glasgow, Glasgow G12 8QW, U.K.

Håvard Rue

Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway

nial{at}stats.gla.ac.uk

havard.rue{at}math.ntnu.no

Received for publication 1 August 2005. Revision received 1 February 2007.
  Abstract

We illustrate how the recursive algorithm of Reeves & Pettitt (2004) for general factorizable models can be extended to allow exact sampling, maximization of distributions and computation of marginal distributions. All of the methods we describe apply to discrete-valued Markov random fields with nearest neighbour integrations defined on regular lattices; in particular we illustrate that exact inference can be performed for hidden autologistic models defined on moderately sized lattices. In this context we offer an extension of this methodology which allows approximate inference to be carried out for larger lattices without resorting to simulation techniques such as Markov chain Monte Carlo. In particular our work offers the basis for an automatic inference machine for such models.

Key Words: Autologistic distribution • Exact sampling • Hidden Markov random field • Ising model • Normalizing constant


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