The Annals of Applied Statistics

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

Emeric Thibaud, Juha Aalto, Daniel S. Cooley, Anthony C. Davison, and Juha Heikkinen

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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.

Article information

Ann. Appl. Stat., Volume 10, Number 4 (2016), 2303-2324.

Received: June 2015
Revised: August 2016
First available in Project Euclid: 5 January 2017

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Global warming likelihood-based inference max-stable process nonstationary extremes partition space-time declustering


Thibaud, Emeric; Aalto, Juha; Cooley, Daniel S.; Davison, Anthony C.; Heikkinen, Juha. Bayesian inference for the Brown–Resnick process, with an application to extreme low temperatures. Ann. Appl. Stat. 10 (2016), no. 4, 2303--2324. doi:10.1214/16-AOAS980.

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Supplemental materials

  • Supplementary Material for “Bayesian inference for the Brown–Resnick process, with an application to extreme low temperatures”. The online supplement provides additional results for the exploratory analysis and the MCMC algorithm used to fit the two Brown–Resnick models, and reports additional diagnostics for the fit of the three models considered in the manuscript.