Bayesian nonparametric spatial modeling with Dirichlet process mixing

• 成果类型: Article
• 署名作者: Gelfand, AE; Kottas, A; MacEachern, SN
• 署名单位: Duke University; University of California System; University of California Santa Cruz; University System of Ohio; Ohio State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214504000002078
• 发表日期: 2005
• 页码: 1021-1035
• 关键词: inference; distributions

摘要

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.