Mike Pitt, Warwick

Title: Bayesian estimation and particle filtering for diffusion driven state space models

Abstract :

We provide methods for carrying out likelihood based inference for a class of diffusion driven state space models. Examples of this class are continuous time stochastic volatility models and counting process models. The problems which are encountered for efficient particle filter methods and for efficient MCMC are highlighted. For both approaches methods are introduced to cambat the degeneracies which would lead to poor performance. The methods we develop are simple to implement and simulation effcient. Importantly, unlike previous methods, the performance of our technique is not worsened, in fact it improves, as the degree of latent augmentation is increased to reduce the bias of the Euler approximation. In addition, our method is not subject to a degeneracy that afflicts previous techniques when the degree of latent augmentation is increased. We also discuss issues of model choice, model checking and filtering. The techniques and ideas are applied to both simulated and real data.