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

TL;DR

This paper develops Bayesian inference methods for the Brown-Resnick process, enabling analysis of environmental extremes like low temperatures, by calculating the full likelihood and applying novel MCMC techniques.

Contribution

It introduces two new Bayesian inference approaches for the Brown-Resnick process, overcoming previous likelihood intractability issues, and applies them to model extreme low temperatures.

Findings

Successful estimation of low temperature extremes in Fennoscandia

Demonstration of full likelihood computation for Brown-Resnick process

Effective use of MCMC with random partitions

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.