Date of Award

Winter 2005

Project Type

Dissertation

Program or Major

Mathematics

Degree Name

Doctor of Philosophy

First Advisor

Ernst Linder

Abstract

This thesis research provides several contributions to computer efficient methodology for estimation with space-time data. First we propose a parsimonious class of computer-efficient Gaussian spatial interaction models that includes as special cases CAR and SAR-like models. This extended class is capable of modeling smooth spatial random fields. We show that, for rectangular lattices, this class is equivalent to higher-order Markov random fields. Thus we capture the computational advantage of iterative updating of Markov random fields, while at the same time provide the possibility of simple interpretation of smooth spatial structure.

This class of spatial models is defined via a spatial structure removing orthogonal transformation, which we propose for any spatial interaction model as a means to improve computation time. Such a transformation is a one-time preprocessing step in iterative estimation, such as in MCMC. For very large data on a rectangular lattice we can achieve further computational savings by circulant embedding which enables use of FFT for calculations. We examine how the model as well as the embedding can be incorporated in hierarchical models for space time data with spatially varying temporal trend components. We describe an application in arctic hydrology where gridded runoff fields are investigated for local trends.

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