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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 2000-24
May 2000

Analysis of spatial data using generalized linear mixed models and Langevin-type Markov chain Monte Carlo


Jesper Møller

Ole F. Christensen, Rasmus Waagepetersen


Markov chain Monte Carlo methods are useful in connection with inference and prediction for spatial generalized linear mixed models, where the unobserved random effects constitute a spatially correlated Gaussian random field. We point out that so-called Langevin-type updates are useful for Metropolis-Hastings simulation of the posterior distribution of the random effects given the data. Furthermore, we discuss the use of improper priors in Bayesian analysis of spatial generalized linear mixed models with particular emphasis on the so-called Poisson-log normal model. For this and certain other models non-parametric estimation of the covariance function of the Gaussian field is also studied. The methods are applied to various data sets including counts of weed plants on a field.

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