Modelling spatially correlated data via mixtures: a Bayesian approach

C Fernández, PJ Green

Research output: Contribution to journalArticle (Academic Journal)peer-review

92 Citations (Scopus)

Abstract

The paper develops mixture models for spatially indexed data. We confine attention to the case of finite, typically irregular, patterns of points or regions with prescribed spatial relationships, and to problems where it is only the weights in the mixture that vary from one location to another. Our specific focus is on Poisson-distributed data, and applications in disease mapping. We work in a Bayesian framework, with the Poisson parameters drawn from gamma priors, and an unknown number of components. We propose two alternative models for spatially dependent weights, based on transformations of autoregressive Gaussian processes: in one (the logistic normal model), the mixture component labels are exchangeable; in the other (the grouped continuous model), they are ordered. Reversible jump Markov chain Monte Carlo algorithms for posterior inference are developed. Finally, the performances of both of these formulations are examined on synthetic data and real data on mortality from a rare disease.
Translated title of the contributionModelling spatially correlated data via mixtures: a Bayesian approach
Original languageEnglish
Pages (from-to)805 - 826
Number of pages22
JournalJournal of the Royal Statistical Society Series B - Statistical Methodology
Volume64 (4)
DOIs
Publication statusPublished - Oct 2002

Bibliographical note

Publisher: Royal Statistical Society

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