# 2019-2020

## 2019/20 Term 1:

### Prof. Terry Lyons FLSW FRSE FRS, University of Oxford

##### MS.02, 2pm-3pm on Tuesday 26th November

Title: What have rough paths got to do with data science?
Abstract: We will survey core features of rough paths and particularly the signature and why they are important to the analysis of streamed data.

## 2019/20 Term 2:

### Prof. Judith Rousseau, University of Oxford

##### OC0.03, 2pm-3pm on Tuesday 25th February

Title: Estimating the interaction functions and the graph of interactions in multivariate Hawkes processes using Bayesian nonparametric methods
Abstract: Hawkes processes form a class of point processes describing self and inter exciting/inhibiting processes. There is now a renewed interest of such processes in applied domains and in machine learning, but there exists only limited theory about inference in such models. To be more precise, the intensity function of a univariate Hawkes process has the following form:

$\lambda(t) = \int_{0}^{t^-} h(t-s) dN_s + \nu$

where $N$ is the Hawkes process and $\nu > 0$. Multivariate Hawkes processes have a similar intensity function which involves the interactions functions between the different components of the process. In this work we propose a generic Bayesian non parametric procedure in such models and we study its theoretical properties, both in terms of the estimation of the parameters which are the impulsions $\nu$ and the interactions functions, and in terms of the graph of interactions. As a consequence of these results we also obtain theoretical guaranties for Bayesian tests on the existence of an interaction (or self excitation) function.

## 2019/20 Term 3:

### This colloquium will postponed to the next academic year

##### MS.01, 2pm-3pm on Wednesday 20th May

Title: TBA
Abstract: TBA.

Current Organisers: Richard Everitt, Jeremie Houssineau

• If you have ideas for possible speakers, then please email one of the organisers above.