TY - JOUR

T1 - Modelling spatially correlated data via mixtures: a Bayesian approach.

AU - Fernandez, Carmen

AU - Green, Peter J.

PY - 2002/10

Y1 - 2002/10

N2 - 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.

AB - 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.

KW - Disease mapping • Grouped continuous model • Logistic normal model • Poisson mixtures • Reversible jump Markov chain Monte Carlo method

U2 - 10.1111/1467-9868.00362

DO - 10.1111/1467-9868.00362

M3 - Journal article

VL - 64

SP - 805

EP - 826

JO - Journal of the Royal Statistical Society: Series B (Statistical Methodology)

JF - Journal of the Royal Statistical Society: Series B (Statistical Methodology)

SN - 1369-7412

IS - 4

ER -