Estimation and model criticism for categorical and Gaussian Markov random fields
MetadataVis full innførsel
We consider two different spatial models to describe the correlation structure on a lateral two dimensional grid. First, a discrete first order Markov random field is studied, where the spatial dependence is represented with the Ising model. Secondly, a continuous Gaussian field is looked upon, which is fitted to a second order Gaussian Markov random field (GMRF) in order to ease the implementation. Different methods for assessing the quality of the two models are performed. We are in possess of real seismic data from the North Sea, and want to find out if the models can explain these satisfactorily. There are many techniques for model checking, but we have only focused on three; comparing the observed data with data predicted by the models, finding the goodness-of-fit using a chi-square statistic, and calculating the Deviance Information Criterion (DIC), which quantifies the trade off between the complexity of a model and how well the model fits some observed data. We test the techniques on synthetic examples, and verify that they work. However, it is harder to tell which model that is best suited to explain the real data from the North Sea. In order to accomplish the model checks, we must estimate the parameters in both models. This task is troublesome for large domains, and different approaches have been considered.