uses a Metropolis-Hastings (MH) step to update the hyperparameters and a Hamiltonian Monte Carlo (HMC) step for the parameters. From the posterior samples we compute a point estimate $(\widehat w_{i1},\ldots,\widehat w_{ip})$ of the weight vector for each node. We follow the approach of @Todeschini2016 and compute a minimum Bayes risk point estimate using a permutation-invariant cost function. Given these point estimates we obtain estimates of the base intensities $\widehat \mu_{ij}$. Posterior inference on the parameters $\phi$ of the Hawkes kernel is then performed using Metropolis-Hastings, as in [@Rasmussen2013]. Details of the two-stage inference procedure are given in the supplementary material.

**Empirical investigation of posterior consistency.** To validate the two-step approximation to the posterior distribution, we study empirically the convergence of our approximate inference scheme using synthetic data. Experiments suggest that the posterior concentrates around the true parameter value. More details are given in the supplementary material.

Experiments {#sec:experiments}
===========

We perform experiments on four temporal interaction datasets from the Stanford Large Network Dataset Collection[^3] [@SNAP2014]:\
$\bullet$ The [Email]{} dataset consists of emails sent within a large European research institution over 803 days. There are 986 nodes, 24929 edges and 332334 interactions. A separate interaction is created for every recipient of 