  Topological data analysis (TDA) studies the shape patterns of data.
Persistent homology (PH) is a widely used method in TDA that summarizes
homological features of data at multiple scales and stores this in persistence
diagrams (PDs). As TDA is commonly used in the analysis of high dimensional
data sets, a sufficiently large amount of PDs that allow performing statistical
analysis is typically unavailable or requires inordinate computational
resources. In this paper, we propose random persistence diagram generation
(RPDG), a method that generates a sequence of random PDs from the ones produced
by the data. RPDG is underpinned (i) by a parametric model based on pairwise
interacting point processes for inference of persistence diagrams and (ii) by a
reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm for generating
samples of PDs. The parametric model combines a Dirichlet partition to capture
spatial homogeneity of the location of points in a PD and a step function to
capture the pairwise interaction between them. The RJ-MCMC algorithm
incorporates trans-dimensional addition and removal of points and
same-dimensional relocation of points across samples of PDs. The efficacy of
RPDG is demonstrated via an example and a detailed comparison with other
existing methods is presented.
