Sampling Conditioned Diffusions

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details:	Martin Hairer, Andrew M. Stuart and Jochen Voss: Sampling Conditioned Diffusions. Pages 159–186 in Trends in Stochastic Analysis, Cambridge University Press, vol. 353 of London Mathematical Society Lecture Note Series, 2009.
online:	link
preprint:	preprint:pdf, preprint:ps
metadata:	BibTeX, MathSciNet, Google
keywords:	MCMC methods, SPDEs

Abstract

For many practical problems it is useful to be able to sample conditioned diffusions on a computer (e.g. in filtering/smoothing to sample from the conditioned distribution of the unknown signal given the known observations). We present a recently developed, SPDE-based method to tackle this problem. The method is an infinite dimensional generalisation of the Langevin sampling technique.

Citations

I believe that this work is cited in the following texts. If you know of any more citations, please let me know.

M. Hairer, A.M. Stuart and J. Voss: Signal Processing Problems on Function Space: Bayesian Formulation, Stochastic PDEs and Effective MCMC Methods. Pages 833–873 in The Oxford Handbook of Nonlinear Filtering, Dan Crisan and Boris Rozovsky (editors), Oxford University Press, 2011.
link, preprint:pdf, more…
J. Voss: The Effect of Finite Element Discretisation on the Stationary Distribution of SPDEs. Submitted, 2011.
arXiv:1110.4653, more…
A. Beskos and A.M. Stuart: Computational complexity of Metropolis-Hastings methods in high dimensions. Pages 61–72 in Proceedings of MCQMC08, Pierre L'Ecuyer and Art B. Owen (editors), 2010.
link
A.M. Stuart: Inverse problems: A Bayesian perspective. Acta Numerica, vol. 19, pp. 451–559, 2010.
DOI:10.1017/S0962492910000061
A. Beskos and A.M. Stuart: MCMC methods for sampling function space. Pages 337–364 in Proceedings of the 6th International Congress on Industrial and Applied Mathematicians (Zürich, 2007), Rolf Jeltsch and Gerhard Wanner (editors), 2009.

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