A Hierarchial Bayesian Model for Spatial Data
Linda Werner
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2000
ISSN 14046342

Abstract:

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 nonlattice 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.


Nyckelord:

MCMC, GMF, Bayesian inference

