Premium
Modelling spatially correlated data via mixtures: a Bayesian approach
Author(s) -
Fernández Carmen,
Green Peter J.
Publication year - 2002
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00362
Subject(s) - markov chain monte carlo , reversible jump markov chain monte carlo , mixture model , prior probability , poisson distribution , bayesian inference , autoregressive model , bayesian probability , computer science , inference , markov chain , count data , gaussian , component (thermodynamics) , mathematics , focus (optics) , algorithm , statistics , artificial intelligence , physics , quantum mechanics , optics , thermodynamics
Summary. 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.