Spatio-temporal Models for Areal Data
in the Exponential Family
Marco Ferreira
Department of Statistics
University of Missouri - Columbia
Friday, February 1, 2008, 12:30–1:30 pm
GEMS classroom, 3rd Floor in
Shriner's Building
Coffee, tea, and cookies will be provided
Abstract
We introduce a class of spatio-temporal models for areal data
in the Exponential Family. This class of models is potentially useful for
the analysis of spatio-temporal medical images and epidemiological processes.
These models assume a latent random field process that evolves through
time with random field convolutions; the convolving fields follow proper
Gaussian Markov random field (PGMRF) processes. At each time, the latent
random field process is related to observations through a link equation.
The use of PGMRF errors brings modeling and computational advantages.
With respect to modeling, it allows time-specific spatial random effects,
as well as spatial dependence for persistent innovation error fields.
Computationally, building on the fact that PGMRF errors have proper density
functions, we have developed an efficient Bayesian estimation procedure
based on Markov chain Monte Carlo with an embedded forward information filter
backward sampler algorithm. Moreover, we have developed simulation-based
spatio-temporal prediction and predictive-density-based model selection
for non-nested spatio-temporal models. We illustrate the use of our
spatio-temporal framework with two datasets. First, we analyze a simulated
spatio-temporal Bernoulli process. Second, we analyze the number of homicides
in Rio de Janeiro State with a spatio-temporal Poison process.