NONPARAMETRIC BAYESIAN ESTIMATION OF MULTIVARIATE HAWKES PROCESSES

Estimation Bayésienne nonparamétrique pour des processus de Hawkes multivariés

Sophie Donnet (1) , Vincent Rivoirard (2) , Judith Rousseau (2)

1 MIA-Paris - Mathématiques et Informatique Appliquées
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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 L1-metrics for stochastic intensities of the Hawkes process. We then deduce rates for the L1-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. Numerical illustrations are then proposed with in mind applications for inferring functional connec-tivity graphs of neurons.

Mots clés: posterior concentration; Bayesian nonparametric; Hawkes processes

Domaines: Statistiques [math.ST]

Sophie Donnet, Vincent Rivoirard, Judith Rousseau. NONPARAMETRIC BAYESIAN ESTIMATION OF MULTIVARIATE HAWKES PROCESSES. 2018. ⟨hal-01710564v1⟩