NONPARAMETRIC BAYESIAN ESTIMATION FOR MULTIVARIATE HAWKES PROCESSES

被引：13

作者：

Donnet, Sophie ^{[1
]}

Rivoirard, Vincent ^{[2
]}

Rousseau, Judith ^{[2
]}

机构：

[1] Univ Paris Saclay, INRA, Paris, France

[2] Univ Paris 09, UMR 7534, CNRS, CEREMADE, Paris, France

来源：

ANNALS OF STATISTICS | 2020年 / 48卷 / 05期

关键词：

Multivariate counting process; Hawkes processes; nonparametric Bayesian estimation; posterior concentration rates; CONVERGENCE-RATES; FUNCTIONAL CONNECTIVITY; POSTERIOR DISTRIBUTIONS; STATISTICAL-MODELS; SPIKE TRAINS; OCCURRENCES; MIXTURES;

D O I：

10.1214/19-AOS1903

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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

引用

页码：2698 / 2727

页数：30

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