### Abstract

In this talk I will give an overview of the problem of conducting Bayesian inference for the fixed parameters of nonlinear multivariate diffusion processes observed partially, discretely, and possibly with error. I will present a sequential strategy based on either SIR or MCMC-based filtering for approximate diffusion bridges, and a "global" MCMC algorithm that does not degenerate as the degree of data augmentation increases. The relationship of these techniques to methods of approximate Bayesian computation will be highlighted.