Open Access
October 2020 Nonparametric Bayesian estimation for multivariate Hawkes processes
Sophie Donnet, Vincent Rivoirard, Judith Rousseau
Ann. Statist. 48(5): 2698-2727 (October 2020). DOI: 10.1214/19-AOS1903


This paper studies nonparametric estimation of parameters of multivariate Hawkes processes. We consider the Bayesian setting and derive posterior concentration rates. First, rates are derived for $\mathbb{L}_{1}$-metrics for stochastic intensities of the Hawkes process. We then deduce rates for the $\mathbb{L}_{1}$-norm of interactions functions of the process. Our results are exemplified by using priors based on piecewise constant functions, with regular or random partitions and priors based on mixtures of Betas distributions. We also present a simulation study to illustrate our results and to study empirically the inference on functional connectivity graphs of neurons


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Sophie Donnet. Vincent Rivoirard. Judith Rousseau. "Nonparametric Bayesian estimation for multivariate Hawkes processes." Ann. Statist. 48 (5) 2698 - 2727, October 2020.


Received: 1 March 2018; Revised: 1 March 2019; Published: October 2020
First available in Project Euclid: 19 September 2020

MathSciNet: MR4152118
Digital Object Identifier: 10.1214/19-AOS1903

Primary: 60G55 , 62G20
Secondary: 62G05

Keywords: Hawkes processes , multivariate counting process , Nonparametric Bayesian estimation , posterior concentration rates

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 5 • October 2020
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