PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

A methodological framework for Monte Carlo probabilistic inference for diffusion processes.
Omiros Papaspiliopoulos
In: Inference and Learning in Dynamic Models, Cambridge University Press (2009) Cambridge University Press .

Abstract

The methodological framework developed and reviewed in this article concerns the \emph{unbiased} Monte Carlo estimation of the transition density of a diffusion process, and the \emph{exact} simulation of diffusion processes. The methodology for unbiased estimation is linked to auxiliary variable methods, and it builds on a rich generic Monte Carlo machinery of simulation of infinite series expansions. This machinery is employed by diverse scientific areas such as population genetics and operational research. The methodology for exact simulation 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.

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EPrint Type:Book Section
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
ID Code:6818
Deposited By:Omiros Papaspiliopoulos
Deposited On:08 March 2010