On block updating in Markov random field models for disease mapping

Leonhard Knorr-Held, Haavard Rue

Research output: Contribution to journalArticlepeer-review

110 Scopus citations

Abstract

Ganssian Markov random field (GMRF) models are commonly used to model spatial correlation in disease mapping applications. For Bayesian inference by MCMC, so far mainly single-site updating algorithms have been considered. However, convergence and mixing properties of such algorithms can be extremely poor due to strong dependencies of parameters in the posterior distribution. In this paper, we propose various block sampling algorithms in order to improve the MCMC performance. The methodology is rather general, allows for non-standard full conditionals, and can be applied in a modular fashion in a large number of different scenarios. For illustration we consider three different applications: two formulations for spatial modelling of a single disease (with and without additional unstructured parameters respectively), and one formulation for the joint analysis of two diseases. The results indicate that the largest benefits are obtained if parameters and the corresponding hyperparameter are updated jointly in one large block. Implementation of such block algorithms is relatively easy using methods for fast sampling of Gaussian Markov random fields (Rue, 2001). By comparison, Monte Carlo estimates based on single-site updating can be rather misleading, even for very long runs. Our results may have wider relevance for efficient MCMC simulation in hierarchical models with Markov random field components.

Original languageEnglish (US)
Pages (from-to)597-614
Number of pages18
JournalScandinavian Journal of Statistics
Volume29
Issue number4
DOIs
StatePublished - Jan 1 2002

Keywords

  • Block updating
  • Disease mapping
  • Hierarchical models
  • Markov chain Monte Carlo
  • Markov random field models
  • Shared component model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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