## The Annals of Applied Statistics

### 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.

#### Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1483606861

Digital Object Identifier
doi:10.1214/16-AOAS980

Mathematical Reviews number (MathSciNet)
MR3592058

Zentralblatt MATH identifier
06688778

#### Citation

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. https://projecteuclid.org/euclid.aoas/1483606861

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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.