Event Details

Statistics seminar in the School of Mathematical Sciences.

Title: Analysing Spatial Point Patterns on Curved Surfaces

Abstract: Statistical methodology for analysing spatial point patterns has traditionally focused on Euclidean settings, particularly planar domains. However, in fields such as microbiology and ecology, such data are increasingly observed on manifolds, where curvature must be accounted for to enable valid inference.

In this seminar, I will focus on the development of Ripley’s K-function, one of the most widely used nonparametric tools for exploratory analysis of spatial point patterns. I will begin with a historical overview of its formulation on planar domains, followed by its extension to spherical settings. I will then present our work extending the K-function to arbitrary convex surfaces, with applications in microbiology, including a multitype formulation that captures interactions between different classes of points. I will conclude with our most recent results on defining the K-function directly on general smooth manifolds (joint work with Scott Ward, Francisco Cuevas, and Rasmus Waagepetersen).

The seminar is designed to be accessible to a broad statistical audience, including those without prior expertise in spatial statistics.