Analyzing Point Processes Using Topological Data Analysis

Overview

Explore the application of topological data analysis in spatial statistics for point process analysis in this 50-minute lecture. Gain insights into standard point process models and learn how topological data analysis techniques can differentiate between them. Discover central limit theorems for topological data analysis-based summary statistics, enabling rigorous statistical analysis. Delve into various point process types, including Poisson, Poisson cluster, Gibbs, and hardcore processes. Examine persistent diagrams and their role in topological data analysis. Review a practical data example and engage with references to deepen understanding. No prior knowledge of point processes is required for this comprehensive overview of the intersection between topological data analysis and spatial statistics.

Syllabus

Introduction
Outline
Point processes
Assumptions
Intensity
Poisson point process
Poisson cluster process
Gibbs point process
Hardcore point process
Topological data analysis
Persistent diagram
Central limit theorem
Data example
References
Questions