Bayesian nonparametric spatial modeling with Dirichlet process mixing

Alan E. Gelfand

doi:10.1198/016214504000002078

Bayesian nonparametric spatial modeling with Dirichlet process mixing

2005-09-01

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AI

DOI：10.1198/016214504000002078

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Customary modeling for continuous point-referenced data assumes a Gaussian process that 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 novel spatial Dirichlet process mixture model to produce a random spatial process that is neither Gaussian nor stationary. We first develop a spatial Dirichlet process model for spatial data and discuss its properties. Because of familiar limitations associated with direct use of Dirichlet process models, we introduce mixing by convolving this process with a pure error process. We then examine properties of models created through such Dirichlet process mixing. In the Bayesian framework, we implement posterior inference using Gibbs sampling. Spatial prediction raises interesting questions, but these can be handled. Finally, we illustrate the approach using simulated data, as well as a dataset involving precipitation measurements over the Languedoc-Roussillon region in southern France.

Keywords:

dependent Dirichlet process

Dirichlet process mixture models

Gaussian process

Markov chain Monte Carlo

nonstationarity

point-referenced spatial data

random distribution

Bayesian nonparametric spatial modeling with Dirichlet process mixing

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