Nonparametric Bayesian Spatial Modeling Using Dependent
Dirichlet Processes

Alan
Gelfand, ISDS, Duke University
(Joint work with A. Kottas, UCSC and S. MacEachern, Ohio State)
Friday, 24 October 2003
3:10 PM
E204 Engineering
ABSTRACT
Customary
modeling for continuous pointreferenced data assumes a
Gaussian
process which is often taken to be stationary. When such
models are
fitted within a Bayesian framework, the unknown parameters
of the process
are assumed to be random so a random Gaussian process
results. Here
we propose a version of a dependent Dirichlet process
mixing model to
produce a random process which is neither Gaussian nor
stationary.
We first develop
a dependent Dirichlet process model for spatial data
and discuss its
properties. Due to familiar limitations associated
with direct use
of Dirichlet process models, we introduce mixing and
examine
properties of models created by such mixing.
Posterior
inference is implemented through familiar Gibbs sampling
which, by now,
is fairly straightforward for Dirichlet process
mixing. Spatial
prediction raises interesting questions but can be
handled.
Finally, we illustrate the approach and the inference
possibilities
through the analysis of simulated datasets as well as
one involving
precipitation measurements over a region in southern
France.
