Modeling and Replicating Persistence Diagrams

Explore the concept of modeling and replicating persistence diagrams in this 41-minute talk by Sarit Agami from the Applied Algebraic Topology Network. Dive into the Replicating Statistical Topology (RST) approach, which provides a parametric model for generating replicated persistence diagrams crucial for statistical inference. Learn about the original RST model and its improved version that accounts for diagram shape, particularly useful when points form clusters. Examine the performance comparison between the refined and original models through various examples. Discover key topics such as bootstrap methods, Gibbs distribution, pseudomaximum likelihood estimation, MCMC, proposal distribution, vertical clustering, and topological signals. Gain insights into the practical applications of these techniques for analyzing and replicating topological features in data.

Introduction
Example
Bootstrap
Gibbs distribution
Treasure of Delta
Pseudomaximum likelihood estimation
MCMC
Replicating persistent diagrams
Proposal distribution
Comparison
Vertical clustering
Results
Topological signals
Backplot