# Sampling Sup-Normalized Spectral Functions for Brown-Resnick Processes

## TL;DR

This paper introduces improved simulation methods for Brown-Resnick processes using spectral functions, optimizing proposal densities for efficiency in MCMC and rejection sampling, with demonstrated performance benefits.

## Contribution

It generalizes existing simulation approaches for Brown-Resnick processes by developing new classes of proposal densities and optimizing their efficiency.

## Key findings

- Enhanced simulation efficiency demonstrated in examples
- Optimal proposal densities identified for MCMC and rejection sampling
- Generalized approaches applicable to spectral functions of max-stable processes

## Abstract

Sup-normalized spectral functions form building blocks of max-stable and Pareto processes and therefore play an important role in modeling spatial extremes. For one of the most popular examples, the Brown-Resnick process, simulation is not straightforward. In this paper, we generalize two approaches for simulation via Markov Chain Monte Carlo methods and rejection sampling by introducing new classes of proposal densities. In both cases, we provide an optimal choice of the proposal density with respect to sampling efficiency. The performance of the procedures is demonstrated in an example.