Some New Random Field Tools for Spatial Analysis

TL;DR

This paper reviews recent advances in the theory of random field geometry, highlighting new formulae for geometric characteristics of excursion sets and discussing interesting applications in spatial analysis.

Contribution

It introduces explicit new formulae for mean values of geometric features of random field excursion sets and discusses their applications.

Findings

New explicit formulae for geometric characteristics

Enhanced understanding of excursion set properties

Applications in spatial analysis and related fields

Abstract

This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric characteristics of excursion sets of random fields. As well as a review of the theory, we provide brief descriptions of some of the more interesting applications.