Bayesian semiparametric modelling of phase-varying point processes

TL;DR

This paper introduces a Bayesian semiparametric method for registering multiple phase-varying point processes, utilizing Bernstein-Dirichlet priors to model mean measures and warp functions, with proven theoretical support and practical effectiveness demonstrated through experiments and real data.

Contribution

It presents a novel Bayesian semiparametric framework for phase-varying point process registration using Bernstein-Dirichlet priors, with theoretical guarantees and practical applications.

Findings

Good performance in numerical experiments

Theoretical support for prior support and consistency

Effective application to climatology data

Abstract

We propose a Bayesian semiparametric approach for registration of multiple point processes. Our approach entails modelling the mean measures of the phase-varying point processes with a Bernstein-Dirichlet prior, which induces a prior on the space of all warp functions. Theoretical results on the support of the induced priors are derived, and posterior consistency is obtained under mild conditions. Numerical experiments suggest a good performance of the proposed methods, and a climatology real-data example is used to showcase how the method can be employed in practice.