Abstract

Diffusion driven models provide natural models for phenomena evolving continuously in time. They appear quite often in various applications across a wide range of diverse scientific areas. The task of likelihood based inference for their parameters is particularly challenging as their infinite dimensional paths can only be observed at a finite number of points and the marginal likelihood for these observations is generally intractable. Things are further complicated by the presence of various observation regimes: the observations may be noisy, partial, from multiple potentially conflicting sources of information, they may correspond to functionals of the diffusion etc. Data augmentation schemes, implemented through MCMC , provide a general unified framework that may in theory handle all such cases. However, extra care is required because usually a suitable reparametrisation is needed to avoid degenerate MCMC algorithms. This talk presents the main features of this framework and illustrates the methodology through various examples.