A Hierarchial Bayesian Model for Spatial Data

Linda Werner

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1404-6342
Spatial datasets are common in the environmental sciences. In this study we have suggested a hierarchical model for a spatial stochastic field. The variation of the stochastic field is modelled as a linear trend plus microvariation in the form of a Gaussian Markov random field, defined on a lattice. To use non-lattice observations we have used a linear binning technique to map the observational points tothe lattice points. To estimate the model parameters we have adopted a Bayesian perspective, and have specified priors for all parameters. Instead of analytical estimation we use Monte Carlo integration over samples made with Markov Chain Monte Carlo simulations, in particular Gibbs sampling. We have used simulated datasets to study how and under what restrictions the estimation procedures perform well. We found some restrictions for the model parameters, and that some of the model parameters are impossible to estimate with small datasets. Also the size of the artificial grid on which the model is set have influence on the quality of the estimation, and must be chosen in consideration of the number of observations. We also suggest ways to continue the investigation.
MCMC, GMF, Bayesian inference