Model Choice and Experimental Design for Generalized Linear Spatial Models

In this paper we look at generalised linear spatial models, in a bayesian setting. For inference we use a special approxomative technique known as the Laplace approximation. We examine a dataset consisting of radionucleide counts sampled over Rongelap Island. The marginal likelihood of a statistical model, can be used as a measure of model quality. Using the Laplace transformation, combined with a special integration technique, we calculate the marginal likelihood for different spatial models. We also discuss spatial designs. We create a set of retrospective designs based on intuition which we compare with a design created by a sequential removal procedure. We use the so called measure of information to compare designs. We calculate the measure of design both based on the real data, and a simulated dataset, which was created using information inferred from the real dataset. We discuss aspects of the individual designs, and how to best calculate the measure of information.