**Date: **Friday 09 June 2017

**Time: **12:45 - 13:30 (Lunch available from 12:35)

**Room:** RA 1501 (Ravelijn)

## Title: Bayesian computation for diffusion processes

** Abstract:**

Diffusion processes are widely used in application areas such as biology and finance. These processes are mathematically defined as solutions to a system of stochastic differential equations of the form

dXt = b(t;Xt) dt + (t;Xt)dWt; X0 = x0 2 Rd:

Here, W is a multivariate Wiener process. Suppose that the process X is discretely observed, say at times 0 = t0 < t1 < ... < tn. The statistical problem consists of inferring the unknown parameter appearing in both the drift coefficient b and diffusion coefficient o. This problem has received much attention over the past two decades and poses a very challenging problem, mainly due to the lack of a closest form expression for the likelihood of the given statistical model.

In this talk I will first position this research problem within computational statistics. Then I will discuss solutions using the Bayesian approach to statistics. I will end with some remaining challenges which are related to ongoing research.

*This concerns joint work with Moritz Schauer (Leiden University), Omiros Papaspiliopoulos (Universitat Pompeu Fabra) and Harry van Zanten (University of Amsterdam).*

[1] Schauer, M. and Van der Meulen, F. H. and Van Zanten, J. H. (2017),Guided proposals for simulating multi-dimensional diusion bridges, Bernoulli 23(4A) (2017), 2917-2950.

[2] Van der Meulen, F. H. and Schauer, M. (2017), Bayesian estimation of discretely observed multi-dimensional diusion processes using guided proposals, Electronic Journal of Statistics 11(1), 2358- 2396.

[3] F.H. van der Meulen and M.R. Schauer (2016) Bayesian estimation of incompletely observed diusions, arXiv:1606.04082.