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Bayesian inference for the Brown-Resnick process, with an application to extreme low temperatures. (English) Zbl 1454.62462
Summary: 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.

62P12 Applications of statistics to environmental and related topics
60G52 Stable stochastic processes
62F15 Bayesian inference
62G32 Statistics of extreme values; tail inference
86A08 Climate science and climate modeling
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