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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2002-3
February 2002

Bayesian analysis of log Gaussian Cox processes for disease mapping


Jesper Møller

Viktor Benes, Karel Bodlák, Rasmus Waagepetersen


We consider a data set of locations where people in Central Bohemia have been infected by tick-borne encephalitis, and where population census data and covariates concerning vegetation and altitude are available. The aims are to estimate the risk map of the disease and to study the dependence of the risk on the covariates. Instead of using the common area l level approaches we consider a Bayesian analysis for a log Gaussian Cox point process with covariates. Posterior characteristics for a discretized version of the log Gaussian Cox process are computed using Markov chain Monte Carlo methods. A particular problem is to determine a model for the population intensity, and the dependence of the results on the model for the population intensity is discussed in detail. Model validation is based on the posterior predictive distribution of various summary statistics.

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