Open Access
December 2016 Bayesian inference for the Brown–Resnick process, with an application to extreme low temperatures
Emeric Thibaud, Juha Aalto, Daniel S. Cooley, Anthony C. Davison, Juha Heikkinen
Ann. Appl. Stat. 10(4): 2303-2324 (December 2016). DOI: 10.1214/16-AOAS980


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.


Download Citation

Emeric Thibaud. Juha Aalto. Daniel S. Cooley. Anthony C. Davison. Juha Heikkinen. "Bayesian inference for the Brown–Resnick process, with an application to extreme low temperatures." Ann. Appl. Stat. 10 (4) 2303 - 2324, December 2016.


Received: 1 June 2015; Revised: 1 August 2016; Published: December 2016
First available in Project Euclid: 5 January 2017

zbMATH: 06688778
MathSciNet: MR3592058
Digital Object Identifier: 10.1214/16-AOAS980

Keywords: Global warming , likelihood-based inference , Max-stable process , nonstationary extremes , Partition , space-time declustering

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.10 • No. 4 • December 2016
Back to Top