BAYESIAN INFERENCE FOR THE BROWN-RESNICK PROCESS, WITH AN APPLICATION TO EXTREME LOW TEMPERATURES

• 成果类型: Article
• 署名作者: Thibaud, Emeric; Aalto, Juha; Cooley, Daniel S.; Davison, Anthony C.; Heikkinen, Juha
• 署名单位: Colorado State University System; Colorado State University Fort Collins; Finnish Meteorological Institute; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Natural Resources Institute Finland (Luke)
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/16-AOAS980
• 发表日期: 2016
• 页码: 2303-2324
• 关键词: likelihood inference; occurrence times; geostatistics; simulation

摘要

The Brown-Resnick max-stable process has proven to be well suited for modeling extremes of complex environmental processes, but in many applications its likelihood function is intractable and inference must be based on a composite likelihood, thereby preventing the use of classical Bayesian techniques. In this paper we exploit a case in which the full likelihood of a Brown-Resnick process can be calculated, using componentwise maxima and their partitions in terms of individual events, and we propose two new approaches to inference. The first estimates the partitions using declustering, while the second uses random partitions in a Markov chain Monte Carlo algorithm. We use these approaches to construct a Bayesian hierarchical model for extreme low temperatures in northern Fennoscandia.