Title: On multidimensional Gaussian Markov random fields and Bayesian computation
Authors: Ying C MacNab - University of British Columbia (Canada) [presenting]
Abstract: Proposals of multivariate Gaussian Markov random field (MGMRF) models have been advanced in tandem with developments of relevant computational solutions and strategies. The symmetric and positivity conditions for a MGMRF, or a class of MGMRFs that are typically defined by full conditionals or as linear models of coregionalization, demand carefully considered parameterization for identification and related computational strategies. Some recent works on MGMRFs are reviewed, with in-depth discussions on strategies for, and challenges in, Bayesian computation. Within the context of analysis of multivariate spatial data on finite lattice in general, and in the context of Bayesian disease mapping and small area estimation in particular, we discuss MGMRFs as prior models or as data models within Bayesian hierarchical model framework. Several examples are presented to illustrate recently proposed computational solutions and unresolved challenges.