Bayesian Inference in Hidden Markov Random Fields for Binary Data Defined on Large Lattices

N. Friel*, A.N. Pettitt, R. Reeves, E. Wit

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

36 Citations (Scopus)
446 Downloads (Pure)

Abstract

Hidden Markov random fields represent a complex hierarchical model, where the hidden latent process is an undirected graphical structure. Performing inference for such models is difficult primarily because the likelihood of the hidden states is often unavailable. The main contribution of this article is to present approximate methods to calculate the likelihood for large lattices based oil exact methods for smaller lattices. We introduce approximate likelihood methods by relaxing some of the dependencies in the latent model, and also by extending tractable approximations to the likelihood, the so-called pseudolikelihood approximations, for a large lattice partitioned into smaller sublattices. Results are presented based oil simulated data as well as inference for the temporal-spatial structure of the interaction between up- and down-regulated states within the mitochondrial chromosome of the Plasmodium falciparum organism. Supplemental material for this article is available online.

Original languageEnglish
Pages (from-to)243-261
Number of pages19
JournalJournal of Computational and Graphical Statistics
Volume18
Issue number2
DOIs
Publication statusPublished - Jun-2009

Keywords

  • Autologistic model
  • Ising model
  • Latent variables
  • Markov chain Monte Carlo methods
  • Normalizing constant
  • MONTE-CARLO
  • MAXIMUM-LIKELIHOOD
  • STOCHASTIC-APPROXIMATION
  • AUTOLOGISTIC REGRESSION
  • NORMALIZING CONSTANTS
  • SPATIAL MODELS
  • IMAGES
  • CLASSIFICATION
  • DISTRIBUTIONS
  • RESTORATION

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