Hierarchical modeling of count data with application to nuclear fall-out |
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Authors: | Birgir Hrafnkelsson Noel Cressie |
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Institution: | (1) deCODE genetics, Sturlugata 8, 101 Reykjavik, Iceland;(2) Department of Statistics, The Ohio State University, 1958 Neil Avenue, 404 Cockins Hall, Columbus, OH, 43210-1247, U.S.A. |
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Abstract: | We propose a method for a Bayesian hierarchical analysis of count data that are observed at irregular locations in a bounded domain of R2. We model the data as having been observed on a fine regular lattice, where we do not have observations at all the sites. The counts are assumed to be independent Poisson random variables whose means are given by a log Gaussian process. In this article, the Gaussian process is assumed to be either a Markov random field (MRF) or a geostatistical model, and we compare the two models on an environmental data set. To make the comparison, we calibrate priors for the parameters in the geostatistical model to priors for the parameters in the MRF. The calibration is obtained empirically. The main goal is to predict the hidden Poisson-mean process at all sites on the lattice, given the spatially irregular count data; to do this we use an efficient MCMC. The spatial Bayesian methods are illustrated on radioactivity counts analyzed by Diggle et al. (1998). |
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Keywords: | Bayesian models calibrating spatial models geostatistics MCMC Markov random fields Poisson random variables spatial prediction spatial priors |
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