14:00 – 15:00 – Iain Souttar (University of Warwick)
Title: Informing algorithms for maximum marginal likelihood estimation: multiscale systems and the method of averaging.
Abstract: In this talk we will present a link between the method of averaging for stochastic differential equations (SDEs) and maximum marginal likelihood estimation (MMLE). The method of averaging relies on the fact that multiscale systems can often be reduced to a single (time-)scale SDE, deriving a so-called averaged system which both qualitatively and quantitatively behaves (under general assumptions) similarly to the multiscale system. With a clever choice of drift and diffusion coefficients, one can find a multiscale system of SDEs reducing, through the method of averaging, to an SDE which itself samples from a distribution concentrated on the maximiser of the marginal likelihood. This multiscale system can then be used as the foundation for a family of algorithms produced through various discretisation schemes, motivating both existing and novel algorithms for MMLE. We will begin this talk with a brief introduction to averaging for SDEs before discussing the link to MMLE. We will then set out some theory underpinning the method of averaging for SDEs, giving a general framework which can be used to prove uniform in time convergence of, among other things, the multiscale system to the desired maximiser. Finally, we will discuss how this link and the averaging literature more widely may be leveraged in the future to inform the future development of algorithms.
Refreshments available between 15:00 – 15:30, Huxley Common Room (HXLY 549)