{"ID":2848981,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.24182","arxiv_id":"2510.24182","title":"Estimation in linear high dimensional Hawkes processes: a Bayesian approach","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.","short_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 $L_1$...","url_abs":"https://arxiv.org/abs/2510.24182","url_pdf":"https://arxiv.org/pdf/2510.24182v1","authors":"[\"Judith Rousseau\",\"Vincent Rivoirard\",\"Déborah Sulem\"]","published":"2025-10-28T08:35:25Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}