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Nonparametric Bayesian estimation of multivariate Hawkes processes

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BNP_Hawkes-HAL-ArXiv.pdf (2.005Mb)
Date
2018
Publishing date
03-2018
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01710564
Dewey
Probabilités et mathématiques appliquées
Sujet
posterior concentration; Bayesian nonparametric; Hawkes processes; Multivariate counting process
URI
https://basepub.dauphine.fr/handle/123456789/17966
Collections
  • CEREMADE : Publications
Metadata
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Author
Donnet, Sophie
135757 Mathématiques et Informatique Appliquées [MIA-Paris]
Rivoirard, Vincent
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Rousseau, Judith
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
57
Abstract (EN)
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.

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