MPS-RR 2000-24

May 2000

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

by:

### 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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