On a generalization of Mat\'ern hard-core processes with applications to max-stable processes

TL;DR

This paper introduces a generalized model of Matérn hard-core processes that unifies various recent approaches, expanding the underlying point process, thinning rules, and marks, with applications to max-stable processes like storm center modeling.

Contribution

It presents a comprehensive generalization of Matérn hard-core processes, connecting them to mixed moving maxima processes and broadening their applicability.

Findings

Unified framework for hard-core processes

Connections to max-stable processes and storm modeling

Enhanced flexibility in point process modeling

Abstract

The Mat\'ern hard-core processes are classical examples for point process models obtained from (marked) Poisson point processes. Points of the original Poisson process are deleted according to a dependent thinning rule, resulting in a process whose points have a prescribed hard-core distance. We present a new model which encompasses recent approaches. It generalizes the underlying point process, the thinning rule and the marks attached to the original process. The new model further reveals several connections to mixed moving maxima processes, e.g. a process of visible storm centres.