Estimation in linear high dimensional Hawkes processes: a Bayesian approach
Statistics Theory
2025-10-29 v1 Statistics Theory
Abstract
In this paper we study the frequentist properties of Bayesian approaches in linear high dimensional Hawkes processes in a sparse regime where the number of interaction functions acting on each component of the Hawkes process is much smaller than the dimension. We consider two types of loss function: the empirical distance between the intensity functions of the process and the norm on the parameters (background rates and interaction functions). Our results are the first results to control the norm on the parameters under such a framework. They are also the first results to study Bayesian procedures in high dimensional Hawkes processes.
Cite
@article{arxiv.2510.24182,
title = {Estimation in linear high dimensional Hawkes processes: a Bayesian approach},
author = {Judith Rousseau and Vincent Rivoirard and Déborah Sulem},
journal= {arXiv preprint arXiv:2510.24182},
year = {2025}
}