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Statistics Seminar

Bayesian nonparametric estimation of the intensities in multivariate Hawkes processes

With Judith Rousseau (Oxford)

Bayesian nonparametric estimation of the intensities in multivariate Hawkes processes

Joint wortk with Sophie Donnet and Vincent Rivoirard.

Hawkes processes are special cases of point processes. In some cases they are also called self excited Poisson processes. Generally speaking, if (N_t, t ∈ [0, T])is the point process, Hawkes processes are caracterised by having a conditional intensity function given by λ(t) = *(ν +int_0^t−
h(t − u)dN_u)_+.

In this work we are interested in estimating the parameters (ν, h) in the context of multivariate Hawkes processes, using Bayesian nonparametric approaches. We propose generic conditions on the true parameters ν, h and the associated prior distributions to obtain posterior concentration rates under the L1 norm for these parameters. We apply these conditions to various families of prior models and finally we present a simulation study in the context of neuroscience.

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