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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
.
AbstractThe 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. [Edit]
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