Explore a method for generating random persistence diagrams (RPDG) in this informative talk. Delve into the underlying parametric model based on pairwise interacting point processes for persistence diagram (PD) inference and the reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm for PD sample generation. Discover how the parametric model combines a Dirichlet partition to capture spatial homogeneity of point locations in a PD with a step function to capture pairwise interactions. Learn about the RJ-MCMC algorithm's incorporation of trans-dimensional addition and removal of points, as well as same-dimensional point relocation across PD samples. Gain insights into material science problems, spatial distribution, interactions, sampling, parameter estimation, confidence intervals, and other related methods. Examine experiments, hypothesis testing, and a comprehensive summary of the RPDG approach.
Farzana Nasrin - Random Persistence Diagram Generator
Applied Algebraic Topology Network via YouTube
Overview
Syllabus
Introduction
Material Science Problem
Goal
Papers
Persistence Diagram
Spatial Distribution
Interactions
Sampling
Algorithm
RPDG
Parameter estimation
Confidence intervals
Other methods
Data set
Experiments
Hypothesis Test
Summary Table
Summary
Taught by
Applied Algebraic Topology Network
