Open Access
2022 Bayesian semiparametric modelling of phase-varying point processes
Bastian Galasso, Yoav Zemel, Miguel de Carvalho
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Electron. J. Statist. 16(1): 2518-2549 (2022). DOI: 10.1214/21-EJS1973


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.

Funding Statement

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.


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Bastian Galasso. Yoav Zemel. Miguel de Carvalho. "Bayesian semiparametric modelling of phase-varying point processes." Electron. J. Statist. 16 (1) 2518 - 2549, 2022.


Received: 1 June 2021; Published: 2022
First available in Project Euclid: 8 April 2022

Digital Object Identifier: 10.1214/21-EJS1973

Keywords: Bernstein–Dirichlet prior , Fréchet mean , phase variation , Point processes , random Bernstein polynomials , Wasserstein distance

Vol.16 • No. 1 • 2022
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