Abstract

Co-authors: Chris Sherlock (Lancaster University)

We consider Bayesian inference for parameters governing nonlinear multivariate diffusion processes using data that may be incomplete, subject to measurement error and observed sparsely in time. We adopt a high frequency imputation approach to inference, by introducing additional time points between observations and working with the Euler-Maruyama approximation over the induced discretisation. We assume that interest lies in the marginal parameter posterior and sample this target via particle MCMC . A vanilla implementation based on a bootstrap filter is eschewed in favour of an auxiliary particle filter where the latent path is extended by sampling a discretisation of a conditioned diffusion. This conditioned diffusion should be carefully constructed to allow for nonlinear dynamics between observations.