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

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.

35 pages; version accepted for publication in Extremes. The final publication is available at http://link.springer.com

References in corpus (2)

• Stationary max-stable fields associated to negative definite functions
• Approximating the conditional density given large observed values via a multivariate extremes framework, with application to environmental data