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.
BG was partially supported by the graduate scholarship 21140901 from the Chilean NSF (CONICYT), YZ was supported by Swiss National Science Foundation Early Postdoc Mobility Fellowship # 178220, and MdC was partially supported by FCT (Fundação para a Ciência e a Tecnologia, Portugal) through the projects PTDC/MAT-STA/28649/2017 and UID/MAT/00006/2019.
We are grateful to the associate editor and two referees for constructive feedback that led to substantial improvement of the paper.
"Bayesian semiparametric modelling of phase-varying point processes." Electron. J. Statist. 16 (1) 2518 - 2549, 2022. https://doi.org/10.1214/21-EJS1973