NONPARAMETRIC BAYESIAN ESTIMATION FOR MULTIVARIATE HAWKES PROCESSES

• 成果类型: Article
• 署名作者: Donnet, Sophie; Rivoirard, Vincent; Rousseau, Judith
• 署名单位: INRAE; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1903
• 发表日期: 2020
• 页码: 2698-2727
• 关键词: CONVERGENCE-RATES; functional connectivity; posterior distributions; STATISTICAL-MODELS; spike trains; occurrences; mixtures

摘要

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 L-1-metrics for stochastic intensities of the Hawkes process. We then deduce rates for the 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