Accelerated Monte Carlo for optimal estimation of time series

Journal of Statistical Physics

Volumn 119, Issue 5-6, 2005, Pages 1331-1345

  Alexander, Francis J ^a   Eyink, Gregory L ^b   Restrepo, Juan M ^c  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b Johns Hopkins University   (United States)

^c University of Arizona   (United States)

Author keywords

Hybrid Monte Carlo; Path integral; Stochastic processes; Time series

Indexed keywords

EID: 23744460629     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-005-3770-1     Document Type: Article

References (44)

1. B. Eraker, MCMC analysis of diffusion processes with application to finance. J. Bus. Econ. Stati., 19-2:177-191, (2001).
2. J. C. Hargreaves and J. D. Annan, Assimilation of paleo-data in a simple earth system model, Clim. Dynam. 19:371-381 (2002).
3. C. Wunsch, The Ocean Circulation Inverse Problem (Cambridge University Press, Cambridge, UK, 1996).
4. E. Kalnay, Atmospheric Modeling, Data Assimilation and Predictability (Cambridge University Press, Cambridge, 2003).
5. J. Liu and C. Sabatti, Simulated sintering: MCMC with spaces of varying dimensions, Bayesian Stat 6:386-413 (1998).
6. J. Liu and C. Sabatti, Generalized Gibbs sampler and multigrid Monte Carlo for Bayesian computation, Biometrika 87:353-369 (2000).
7. H. Sorensen, Parametric inference for diffusion processes observed at discrete points in time: A survey. Internat. Statist. Rev. 72(3):337-354 (2004).
8. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter eds. Markov Chain Monte Carlo in Practice. (Chapman and Hall, New York, 1996).
9. Chen, Bayesian filtering: From Kalman filters to particle filters and beyond, McMaster University Technical Report, 2003.
10. J. S. Liu, Monte Carlo Strategies in Scientific Computing (Springer, New York, 2001).
11. M-H. Chen, Q-M. Shao, and J. G. Ibrahim, Monte Carlo Methods in Bayesian Computation, (Springer-Verlag, New York, Berlin, 2000).
12. B. Pendleton S. Duane, A. D. Kennedy, and D. Roweth, Hybrid Monte Carlo, Phys. Lett. B. 195:216-222 (1987).
13. R. M. Neal, Probabilistic inference using Markov chain Monte Carlo methods, Technical Report CRG-TR-93-1, Dept. of Computer Science, University of Toronto, 1993.
14. R. Toral and A. L. Ferreira, A general class of hybrid Monte Carlo methods. (Proceedings of Physics Computing 94, pp. 265-268, 1994).
15. A. D. Kennedy and B. Pendelton, Cost of the generalised hybrid Monte Carlo algorithm for free field theory, Nucl. Phys. B, B607:456-510 (2001).
16. R. Salazar and R. Toral, Simulated annealing using hybrid Monte Carlo, J. Stat. Phys., 89:1047-1060 (1997).
17. R. Salazar and R. Toral, Hybrid simulated annealing, J. Stat. Phys. 89:1047 (1997).
18. A. Gelb. Applied Optimal Estimation (MIT Press, Cambridge, MA, 1974).
19. H. Tanizaki, Nonlinear Filters: Estimation and Applications (Springer-Verlag, New York, 1996).
20. P. Del Moral, Feynman-Kac Formulae (Springer-Verlag, New York, 2004).
21. A. Doucet, N. de Freitas, and N. Gordon, Sequential Monte Carlo Methods in Practice (Springer-Verlag, New York, 2002).
22. R. L. Stratonovich, Conditional Markov processes, Theor. Prob. Appl. 5:156-178 (1960).
23. H. J. Kushner, On the differential equations satisfied by conditional probability densities of Markov processes, with applications, J. SIAM Control Ser.A 2:106-119 (1962).
24. H. J. Kushner, Dynamical equations for optimal nonlinear filtering, J. Diff. Eq. 3:179-190 (1967).
25. E. Pardoux, Équations du filtrage non linéaire de la prédiction et du lissage, Stochastics 6:193-231 (1982).
26. G. L. Eyink, J. M. Restrepo, and F. J. Alexander, A mean field approximation in data assimilation for nonlinear dynamics, Physica D 194:347-368 (2004).
27. P. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer-Verlag, Berlin, 1992).
28. F. Langouche, D. Roeckaerts, and E. Tirapegui, On the most probable path for diffusion processes, J. Phys. A 11:L263-L268 (1978).
29. R. Graham, Path integral formulation of general diffusion processes, Zeitschrift fur Physik 26:281-290, (1977).
30. F. Langouche, D. Roeckaerts, and E. Tirapegui, Functional integral methods for stochastic fields, Physica 95A:252-274 (1979).
31. Thomas A. Severini, Likelihood Methods in Statistics (Oxford University Press, New York, 2001).
32. O. Talagrand and P. Courtier, Variational assimilation of meteorological observations with the adjoint vorticity equation. I: Theory, Quart. J. Roy. Meteor. Soc. 113:1311-1328 (1987).
33. J. Goodman and A. D. Sokal, Multigrid Monte Carlo method. Conceptual foundations, Phys. Rev. D 40:2035-2071 (1989).
34. R. H. Swendsen and J. S. Wang, Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett. 58:86-88 (1987).
35. E. Domany and D. Kandel, General cluster Monte Carlo dynamics, Phys. Rev. B 43:8539 (1991).
36. G. G. Batrouni, G. R. Katz, A. S. Kronfeld, G. P. Lepage, B. Svetitsky, and K. G. Wilson, Langevin simulations of lattice field theories, Phys. Rev. D 32:2736-2747 (1985).
37. F. J. Alexander, B. M. Boghosian, R. C. Brower, and S. R. Kimura, Fourier acceleration of langevin molecular dynamics, Phys. Rev. E 066704 (2001).
38. S. Caterall and S. Karamov, Testing a Fourier accelerated hybrid Monte Carlo algorithm, Phys. Lett. B B528:301-305 (2002).
39. R. Toral and A. Ferreira, Hybrid Monte Carlo method for conserved-order-parameter systems, Phys. Rev. E 47:3848-3851 (1993).
40. R. N. Miller, M. Ghil, and P. Gauthiez, Advanced data assimilation in strongly nonlinear dynamical systems, J. Atmos. Sci. 51:1037-1056 (1994).
41. G. L. Eyink and J. R. Restrepo, Most probable histories for nonlinear dynamics: Tracking climate transitions, J. Stat. Phys. 101:459-472 (2000).
42. S. Godsill, A. Doucet, and M. West, Monte carlo smoothing for non-linear time series, (2001). URL: citeseer.ist.psu.edu/godsill01monte.html.
43. G. L. Eyink, J. M. Restrepo, and F. J. Alexander, Reducing computational complexity using closures in a mean field approach in data assimilation, submitted (2002).
44. A. Bennett, Inverse Modeling of the Ocean and Atmosphere (Cambridge University Press, Cambridge, UK, 2002).