Inference and Filtering for Partially Observed Diusion Processes via Sequential Monte Carlo
Edward L. Ionides · 2003
Diusion processes observed partially or discretely, possibly with observa- tion error, arise when constructing stochastic models in continuous time. The method of Sequential Monte Carlo provides an alternative to Markov Chain Monte Carlo methods, and can be eective in complex models at the cutting edge of scientific research. This paper introduces Sequential Monte Carlo ap- proaches to inference for partially observed diusion processes. New methods for solving the filtering, predicting and smoothing problems are developed. Two new filtering algorithms are compared with existing meth- ods on a nonlinear problem for which a closed form solution exists. A novel measure of filter accuracy helps to highlight strengths and weaknesses of the methods.