Bayesian nonparametric spatial modeling with dirichlet process mixing

  • Gelfand A
  • Kottas A
  • Maceachern S
  • 96


    Mendeley users who have this article in their library.
  • 173


    Citations of this article.


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.

Author-supplied keywords

  • Dependent Dirichlet process
  • Dirichlet process mixture models
  • Gaussian process
  • Markov chain Monte Carlo
  • Nonstationarity
  • Point-referenced spatial data
  • Random distribution

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • Alan E. Gelfand

  • Athanasios Kottas

  • Steven N. Maceachern

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free