The Method of Batch Inference for Multivariate Diffusions

Diffusion processes have been used to model a variety of continuous-time phenomena in Finance, Engineering, and the Natural Sciences. However, parametric inference has long been complicated by an intractable likelihood function, the solution of a partial differential equation. For many multivariate models, the most effective inference approach involves a large amount of missing data for which the typical Gibbs sampler can be arbitrarily slow. On the other hand, a recent method of joint parameter and missing data proposals can lead to a radical improvement, but their acceptance rate scales exponentially with the number of observations.