A full Bayesian framework is illustrated. The R-packages estimate the posteriors and classify any dataset converted to persistence diagrams.

Persistence diagrams offer a way to summarize topological and geometric properties latent in datasets. While several methods have been developed that utilize persistence diagrams in statistical inference, a full Bayesian treatment remains absent. We, relying on the theory of point processes, lays the foundation for Bayesian inference with persistence diagrams. We model persistence diagrams as point processes with prior distribution and compute posterior distribution by adopting techniques from the theory of marked point processes. We then propose a family of conjugate priors via Gaussian mixtures and compute the posterior in light of observed persistence diagrams. We also present Bayes factor classification algorithm depending on the posteriors estimated.

Readers are refered to the following article for more details: Bayesian Inference for Persistent Homology, V Maroulas, F Nasrin, C Oballe, arXiv:1901.02034, 2019.