Inference and Filtering for Partially Observed Diffusion Processes via Sequential Monte Carlo

• Activity Number: 80
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Edward Ionides*+
• Companies: University of Michigan
• Keywords: discrete time sampling ; inference for stochastic processes ; nonlinear diffusion ; particle filter ; stochastic differential equation

Abstract

Stochastic models involving discrete time sampling of an underlying continuous time process, possibly with observation error, arise in many fields. When the underlying process is Markov and has continuous sample paths, the model is called a partially observed diffusion process. Questions of interest include reconstruction of the unobserved process and estimation of unknown model parameters. Sequential Monte Carlo (SMC), also known as the Particle Filter, is a technique which has been applied to various partially observed Markov models. This work investigates a new class of SMC algorithms which takes advantage of special properties of diffusion processes. Transition densities of nonlinear diffusions and conditional nonlinear diffusions are hard to calculate, however diffusion processes are easy to simulate from. Likelihood ratios are also easy to calculate. Questions are raised concerning the mixing properties of the "particles" for which the new algorithms differ from standard SMC, and the somewhat surprising ability of the new algorithms to function when the observation error is low or singular.