Some problems in multivariate spatial and spatio-temporal modeling

Date of Completion

January 2004






This thesis addresses some problems in multivariate spatial and spatio-temporal modeling using a bayesian approach. The data are point referenced in a region. The thesis comprises three main parts. The first part discusses problems in spatio-temporal change-point modeling by introducing separable spatio-temporal covariance functions that change with time, thus addressing the change of various features in the model, namely, mean, variance and correlation. The second part of the thesis uses the famous Olcott Chicago land value data to examine and analyze two years of land values. It also develops distributions of gradients on the surface and uses that to study certain second order behavior of the response surfaces. The third part develops novel cross-covariance functions by convolving stationary covariance functions to model valid multivariate spatial models. An environmental dataset obtained from the California Air Resources Board is used to analyze and compare the performance of this model with the existing model of coregionalization (Wackernagel, 2003). ^