Conditional Path Sampling of SDEs and the Langevin MCMC Method
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Andrew M. Stuart, Jochen Voss and Petter Wiberg:
Conditional Path Sampling of SDEs and the Langevin MCMC Method.
Communications in Mathematical Sciences, vol. 2, no. 4,
pp. 685–697, 2004.
We introduce a stochastic PDE based approach to sampling paths of SDEs,
conditional on observations. The SPDEs are derived by generalising the
Langevin MCMC method to infinite dimensions. Various applications are
described, including sampling paths subject to two end-point conditions
(bridges) and nonlinear filter/smoothers.
Citations
I believe that this work is cited in the following texts.
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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…
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
J. Weare:
Particle filtering with path sampling and an application to a bimodal ocean current model.
Journal of Computational Physics, vol. 228, no. 12,
pp. 4312–4331, 2009.
DOI:10.1016/j.jcp.2009.02.033
M. Hairer, A.M. Stuart and J. 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.
link, preprint:pdf, more…
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.
Y. Efendiev and T.Y. Hou:
Multiscale Finite Element Methods: Theory and Applications.
Springer, 2009.
A. Beskos, G.O. Roberts, A.M. Stuart and J. Voss:
MCMC Methods for Diffusion Bridges.
Stochastics and Dynamics, vol. 8, no. 3, pp. 319–350,
2008.
DOI:10.1142/S0219493708002378, preprint:pdf, more…
E. Cancès, C. Le Bris and P.-L. Lions:
Molecular simulation and related topics: some open mathematical problems.
Nonlinearity, vol. 21, no. 9, pp. T165–T176, 2008.
DOI:10.1088/0951-7715/21/9/T03
M. Castro and G. Lythe:
Numerical experiments on noisy chains: from collective
transitions to nucleation-diffusion.
SIAM J. Appl. Dyn. Syst., vol. 7, no. 1, pp. 207–219,
2008.
DOI:10.1137/070695514
T. Müller-Gronbach and K. Ritter:
Minimal errors for strong and weak approximation of stochastic differential equations.
Pages 53–82 in Monte Carlo and Quasi-Monte Carlo Methods 2006,
A. Keller, S. Heinrich and H. Niederreiter (editors), 2008.
link
M. Hairer, A.M. Stuart and J. Voss:
Analysis of SPDEs Arising in Path Sampling, Part II: The Nonlinear Case.
Annals of Applied Probability, vol. 17, no. 5,
pp. 1657–1706, 2007.
DOI:10.1214/07-AAP441, arXiv:math/0601092, more…
A. Apte, M. Hairer, A.M. Stuart and J. Voss:
Sampling The Posterior: An Approach to Non-Gaussian Data Assimilation.
Physica D: Nonlinear Phenomena, vol. 230, no. 1–2,
pp. 50–64, 2007.
DOI:10.1016/j.physd.2006.06.009, preprint:pdf, more…
T. Lelièvre, M. Rousset and G. Stoltz:
Computation of free energy differences through nonequilibrium
stochastic dynamics: the reaction coordinate case.
J. Comput. Phys., vol. 222, no. 2, pp. 624–643, 2007.
MR2313418
T.F. Miller III and C. Predescu:
Sampling diffusive transition paths.
Journal of Chemical Physics, vol. 126, no. 14, 2007.
arXiv:cond-mat/0610597
R. van Handel:
Filtering, Stability, and Robustness.
PhD thesis, California Institute of Technology, Passadena, California, 2007.
A. Beskos, O. Papaspiliopoulos and G.O. Roberts:
Retrospective exact simulation of diffusion sample paths with applications.
Bernoulli, vol. 12, no. 6, pp. 1077–1098, 2006.
MR2274855
M. Hairer, A.M. Stuart, J. Voss and P. Wiberg:
Analysis of SPDEs arising in Path Sampling, Part I: The Gaussian Case.
Communications in Mathematical Sciences, vol. 3, no. 4,
pp. 587–603, 2005.
link, arXiv:math/0601095, more…