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 point-referenced 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.

 

 

 


 

 

 

College of Natural Sciences


 

 

 

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