Non-parametric Bayesian estimation for Hawkes processes.

Summary Multidimensional Hawkes processes are used to model neuronal action potentials. The estimation of intensity functions allows to understand the interaction structure of neurons. The non-parametric estimation of these functions has been proposed by LASSO type methods in a frequentist framework. We are interested in their non-parametric estimation in a Bayesian framework. For this purpose, we implement algorithms of the Sequential Monte Carlo Sampler type, particularly adapted to these point processes. Multidimensional Hawkes processes are used to modelise multivariate neuron spike data.