Krzysztof Łatuszyński (University of Warwick)

Exact Bayesian inference for discretely observed jump-diffusions

The standard approach to inference for parametric diffusion processes
relies on discretisation techniques (such as the Euler method) that
introduce an approximation error difficult to quantify especially for
discontinuous models, like jump-diffusions.
In this talk, I will present methodology for exact inference that
avoids discretisation errors and allows to design MCMC samplers
targeting the exact posterior distribution of the diffusion parameters
and diffusion path between observations. The approach is based on
Bernoulli Factory type subroutines, and is a general alternative to
pseudo-marginal inference. The talk will be based on
http://imstat.org/bjps/papers/BJPS374.pdf  and
https://arxiv.org/pdf/1707.00332.pdf   and is joint work with Flavio
Goncalves and Gareth Roberts.