Conditional simulation of extremal Gaussian processes

TL;DR

This paper develops a method for accurately simulating conditional realizations of a specific class of extremal Gaussian processes, enabling better modeling of extreme events like temperature spikes.

Contribution

It derives the conditional distributions for Schlather's max-stable process and adapts existing algorithms for practical, accurate conditional simulation.

Findings

The method provides accurate conditional simulations.

It handles real-sized datasets effectively.

Application to Swiss temperature extremes demonstrates practical utility.

Abstract

Recently the regular conditional distributions of max-infinitely divisible processes were derived by \citet{Dombry2011} and although these conditional distributions have complicated closed forms, \citet{Dombry2011b} introduce an algorithm to get conditional realizations of Brown-Resnick processes. In this paper we derive the regular conditional distributions of the max-stable process introduced by \citet{Schlather2002} and adapt the framework of \citet{Dombry2011b} to this specific process. We test the methods on simulated data and give an application to extreme temperatures in Switzerland. Results show that the proposed sampling scheme provide accurate conditional simulations and can handle real-sized problems.