Bayesian nonparametric spatial modeling with dirichlet process mixing

Published

Journal Article (Review)

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. © 2005 American Statistical Association.

Full Text

Duke Authors

Cited Authors

  • Gelfand, AE; Kottas, A; Maceachern, SN

Published Date

  • September 1, 2005

Published In

Volume / Issue

  • 100 / 471

Start / End Page

  • 1021 - 1035

International Standard Serial Number (ISSN)

  • 0162-1459

Digital Object Identifier (DOI)

  • 10.1198/016214504000002078

Citation Source

  • Scopus