Conditional Sampling for Max-Stable Processes with a Mixed Moving Maxima Representation

TL;DR

This paper presents an exact conditional sampling method for stationary max-stable processes with mixed moving maxima representations, applicable to processes like Smith and Brown-Resnick, with competitive computational performance.

Contribution

It introduces a novel exact sampling algorithm based on Poisson point processes for max-stable processes, including approximation techniques for complex shape functions.

Findings

Algorithm successfully applied to Smith and Brown-Resnick processes.

The proposed method is computationally competitive with existing approaches.

Approximation techniques extend applicability to general shape functions.

Abstract

This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using the Poisson point process structure of such processes. For explicit calculations we restrict ourselves to the one-dimensional case and use a finite number of shape functions satisfying some regularity conditions. For more general shape functions approximation techniques are presented. Our algorithm is applied to the Smith process and the Brown-Resnick process. Finally, we compare our computational results to other approaches. Here, the algorithm for Gaussian processes with transformed marginals turns out to be surprisingly competitive.