  Topological data analysis (TDA) studies the shape patterns of data.
Persistent homology is a widely used method in TDA that summarizes homological
features of data at multiple scales and stores them in persistence diagrams
(PDs). In this paper, we propose a random persistence diagram generator (RPDG)
method that generates a sequence of random PDs from the ones produced by the
data. RPDG is underpinned by a model based on pairwise interacting point
processes, and a reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm.
A first example, which is based on a synthetic dataset, demonstrates the
efficacy of RPDG and provides a comparison with another method for sampling
PDs. A second example demonstrates the utility of RPDG to solve a materials
science problem given a real dataset of small sample size.
