Bayesian inference for the Brown-Resnick process, with an application to extreme low temperatures

Abstract

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.

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• The pseudo-marginal approach for efficient Monte Carlo computations
• Statistical Modeling of Spatial Extremes
• Stationary max-stable fields associated to negative definite functions
• Extremes on river networks
• Efficient inference and simulation for elliptical Pareto processes
• Bayesian inference for the Brown-Resnick process, with an application to extreme low temperatures
• Anisotropic Brown-Resnick space-time processes: estimation and model assessment

Cited by in corpus (4)

• Bayesian inference for the Brown-Resnick process, with an application to extreme low temperatures
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