NONPARAMETRIC BAYESIAN ESTIMATION OF MULTIVARIATE HAWKES PROCESSES

Abstract : 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.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01710564
Contributeur : Vincent Rivoirard <>
Soumis le : vendredi 23 mars 2018 - 21:15:04
Dernière modification le : vendredi 30 mars 2018 - 01:26:25

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  • HAL Id : hal-01710564, version 2
  • ARXIV : 1802.05975

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Sophie Donnet, Vincent Rivoirard, Judith Rousseau. NONPARAMETRIC BAYESIAN ESTIMATION OF MULTIVARIATE HAWKES PROCESSES. 2018. 〈hal-01710564v2〉

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