Date of Award
Doctor of Philosophy
Petruta C. Caragea
Mark S. Kaiser
A multivariate Markov random field (MRF) model can be an appealing approach to an analysis of spatially correlated data, where multiple responses at each location may contain complex dependence structures, both across and within the areal units. To develop such a model, a functional form of the conditional distribution (with dependence parameters) for the multiple random variables must be determined. In this work, we study alternative formulations of a bivariate Gaussian MRF which are distinguished by choice of spatial or non-spatial neighborhood structures. We then consider a problem of MRF model assessments to diagnose the adequacy of the model structure (e.g., spatial neighborhood) for observed spatial data. We develop a procedure for assessing a particular dependence structure made in bivariate MRF model formulation, using the method of spatial blockwise empirical likelihood (SBEL). Simulation studies show that the proposed SBEL method provides a way to detect an incorrect assumption of the conditional dependence structure used in bivariate model construction. This procedure is also illustrated with an example of the daily average temperatures and dew points measured in Iowa during 2016.
Seo, Yeon-Jung, "Selection and assessment of bivariate Markov random field models" (2018). Graduate Theses and Dissertations. 17311.