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arXiv · 2510.24182

Estimation in linear high dimensional Hawkes processes: a Bayesian approach

Judith Rousseau·Vincent Rivoirard·Déborah Sulem
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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 $L_1$ distance between the intensity functions of the process and the $L_1$ norm on the parameters (background rates and interaction functions). Our results are the first results to control the $L_1$ norm on the parameters under such a framework. They are also the first results to study Bayesian procedures in high dimensional Hawkes processes.

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Judith Rousseau, Vincent Rivoirard, Déborah Sulem. 2025-10-28. Estimation in linear high dimensional Hawkes processes: a Bayesian approach. https://arxiv.org/abs/2510.24182

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