Andrew Golightly (University of Newcastle)
Building bridges: Improved bridge constructs for stochastic differential equations
Hicks Lecture Theatre C, 2pm
We consider the task of generating discrete-time realisations of a non-linear multivariate
diffusion process satisfying an Ito stochastic differential equation conditional
on an observation taken at a fixed future time-point. Such realisations are typically termed
diffusion bridges. Since, in general, no closed form expression exists for the transition
densities of the process of interest, a widely adopted solution works with the Euler-Maruyama
approximation, by replacing the intractable transition densities with Gaussian approximations.
However, the density of the conditioned discrete-time process remains intractable, necessitating
the use of computationally intensive methods such as Markov chain Monte Carlo. Designing an
efficient proposal mechanism which can be applied to a noisy and partially observed system
that exhibits non-linear dynamics is a particularly challenging problem, and is the focus of this talk.
By partitioning the process into two parts, one that accounts for non-linear dynamics in
a deterministic way, and another as a residual stochastic process, we develop a class of
novel constructs that bridge the residual process via a linear approximation. As well as
compare the performance of each new construct with a number of existing approaches, we
illustrate the methodology in a real data application.