Conditional Sampling for Spectrally Discrete Max-Stable Random Fields

TL;DR

This paper introduces an explicit formula and an efficient algorithm for conditional sampling in spectrally discrete max-stable random fields, enhancing statistical inference for spatial extreme value modeling.

Contribution

It provides a novel explicit conditional probability formula and an exact sampling algorithm for a broad class of max-stable random fields, improving prediction methods.

Findings

Developed an explicit formula for conditional probabilities in max-linear models.

Created an efficient algorithm for exact conditional sampling.

Applied methods to spatial extreme value prediction in environmental sciences.

Abstract

Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a consequence, we develop an algorithm for efficient and exact sampling from the conditional distributions. Our method provides a computational solution to the prediction problem for spectrally discrete max-stable random fields. This work offers new tools and a new perspective to many statistical inference problems for spatial extremes, arising, for example, in meteorology, geology, and environmental applications.