  Multivariate point processes are widely applied to model event-type data such
as natural disasters, online message exchanges, financial transactions or
neuronal spike trains. One very popular point process model in which the
probability of occurrences of new events depend on the past of the process is
the Hawkes process. In this work we consider the nonlinear Hawkes process,
which notably models excitation and inhibition phenomena between dimensions of
the process. In a nonparametric Bayesian estimation framework, we obtain
concentration rates of the posterior distribution on the parameters, under mild
assumptions on the prior distribution and the model. These results also lead to
convergence rates of Bayesian estimators. Another object of interest in
event-data modelling is to recover the graph of interaction - or Granger
connectivity graph - of the phenomenon. We provide consistency guarantees on
Bayesian methods for estimating this quantity; in particular, we prove that the
posterior distribution is consistent on the graph adjacency matrix of the
process, as well as a Bayesian estimator based on an adequate loss function.
