A methodological framework for Monte Carlo probabilistic inference for diffusion processes
Date: June 2009
Abstract: The methodological framework developed and reviewed in this article concerns the unbiased Monte Carlo estimation of the transition density of a diffusion process, and the exact simulation of diffusion processes. The former relates to auxiliary variable methods, and it builds on a rich generic Monte Carlo machinery of unbiased estimation and simulation of infinite series expansions which relates to techniques used in diverse scientific areas such as population genetics and operational research. The latter is a recent significant advance in the numerics for diffusions, it is based on the so-called Wiener-Poisson factorization of the diffusion measure, and it has interesting connections to exact simulation of killing times for the Brownian motion and interacting particle systems, which are uncovered in this article. A concrete application to probabilistic inference for diffusion processes is presented by considering the continuous-discrete non-linear filtering problem.