Nonparametric Bayesian inference for the spectral density function of a random field

• 成果类型: Article
• 署名作者: Zheng, Yanbing; Zhu, Jun; Roy, Anindya
• 署名单位: University of Kentucky; University of Wisconsin System; University of Wisconsin Madison; University System of Maryland; University of Maryland Baltimore County
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asp066
• 发表日期: 2010
• 页码: 238245
• 关键词: dirichlet; mixtures

摘要

A powerful technique for inference concerning spatial dependence in a random field is to use spectral methods based on frequency domain analysis. Here we develop a nonparametric Bayesian approach to statistical inference for the spectral density of a random field. We construct a multi-dimensional Bernstein polynomial prior for the spectral density and devise a Markov chain Monte Carlo algorithm to simulate from the posterior of the spectral density. The posterior sampling enables us to obtain a smoothed estimate of the spectral density as well as credible bands at desired levels. Simulation shows that our proposed method is more robust than a parametric approach. For illustration, we analyse a soil data example.