A new metric between distributions of point processes

By Dominic Schuhmacher, Aihua Xia. Advances in Applied Probability, 2007

53 citations recorded by the source corpus.

Most metrics between finite point measures currently used in the literature have the flaw that they do not treat differing total masses in an adequate manner for applications. This paper introduces a new metric d̅ 1 that combines positional differences of points under a closest match with the relative difference in total mass in a way that fixes this flaw. A comprehensive collection of theoretical results about d̅ 1 and its induced Wasserstein metric d̅ 2 for point process distributions are given, including examples of useful d̅ 1-Lipschitz continuous functions, d̅ 2 upper bounds for the Poisson process approximation, and d̅ 2 upper and lower bounds between distributions of point processes of independent and identically distributed points. Furthermore, we present a statistical test for multiple point pattern data that demonstrates the potential of d̅ 1 in applications.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0f32e9092eb54b570098d3d88a5162d7dcd203d9

Citations in the corpus

• Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry (2014, unknown): “tion), one often uses weaker notions of distance. Starting with the work of Barbour and Brown [4] and 2 Barbour, Holst and Janson [8], this has been done by Brown, Chen, Schuhmacher, Weinberg and Xia [11, 12, 13, 15, 39, 40, 42]. Our work goes in the opposite direction since the KantorovichRubinstei”
• Spatial logistic regression and change-of-support in Poisson point processes (2010, unknown): “See [71] for an equivalent metric d̄2 ≤ d2.”