Sampling sup‐normalized spectral functions for Brown–Resnick processes. Issue 1 (6th May 2019)

• Record Type: Journal Article
• Authors: Oesting, Marco; Schlather, Martin; Schillings, Claudia
• Is Part Of: Stat. Volume 8:Issue 1 (2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-05-06
• Subjects: Markov chain Monte Carlo -- max‐stable process -- Pareto process -- rejection sampling -- spatial extremes; Statistics -- Periodicals; 519.2
• DOI: 10.1002/sta4.228
• Languages: English
• ISSNs: 2049-1573

Abstract

Abstract : Sup‐normalized spectral functions form building blocks of max‐stable and Pareto processes and therefore play an important role in modelling 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.