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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 L1L_1 distance between the intensity functions of the process and the L1L_1 norm on the parameters (background rates and interaction functions). Our results are the first results to control the L1L_1 norm on the parameters under such a framework. They are also the first results to study Bayesian procedures in high dimensional Hawkes processes.

Keywords

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}
}
R2 v1 2026-07-01T07:09:10.841Z