Bayesian geostatistical modelling with informative sampling locations

• 成果类型: Article
• 署名作者: Pati, D.; Reich, B. J.; Dunson, D. B.
• 署名单位: Duke University; North Carolina State University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asq067
• 发表日期: 2011
• 页码: 3548
• 关键词: posterior consistency

摘要

We consider geostatistical models that allow the locations at which data are collected to be informative about the outcomes. A Bayesian approach is proposed, which models the locations using a log Gaussian Cox process, while modelling the outcomes conditionally on the locations as Gaussian with a Gaussian process spatial random effect and adjustment for the location intensity process. We prove posterior propriety under an improper prior on the parameter controlling the degree of informative sampling, demonstrating that the data are informative. In addition, we show that the density of the locations and mean function of the outcome process can be estimated consistently under mild assumptions. The methods show significant evidence of informative sampling when applied to ozone data over Eastern U.S.A.