Parameter estimation for partially observed hypoelliptic diffusions

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 71, Issue 1, 2009, Pages 49-73

  Pokern, Yvo ^a   Stuart, Andrew M ^a   Wiberg, Petter ^b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b Goldman Sachs Group   (United States)

Author keywords

Gibbs sampler; Hypoelliptic diffusion; Numerical methods; Parameter estimation; Partial observation

Indexed keywords

EID: 58149347586     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2008.00689.x     Document Type: Article

References (25)

1. Breton, A. L. Musiela, M. (1985) Some parameter estimation problems for hypoelliptic homogeneous gaussian diffusions. Seq. Meth. Statist., 22, 337 356.
2. Brooks, B. R. (1983) Charmm: a program for macromolecular energy, minimization and dynamics calculations. J. Computnl Chem., 4, 187 217.
3. Catlin, D. E. (1989) Estimation, Control and the Discrete Kalman Filter. New York : Springer.
4. Dempster, A. P., Laird, N. M. Rubin, D. B. (1977) Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. R. Statist. Soc. B, 39, 1 38.
5. Durrett, R. (1996) Stochastic Calculus - a Practical Introduction. London : CRC Press.
6. Fischer, A. (1997) Die hybride Monte-Carlo-Methode in der Molekülphysik. Diplomarbeit. Frei Universität, Berlin.
7. Gaines, J. G. Lyons, T. J. (1997) Variable step size control in the numerical solution of stochastic differential equations. SIAM J. Appl. Math., 57, 1455 1484.
8. Gardiner, C. W. (1985) Handbook of Stochastic Methods. New York : Springer.
9. Giannopoulos, P. Godsill, S. J. (2001) Estimation of car processes observed in noise using bayesian inference. In Proc. Int. Conf. Acoustics, Speech and Signal Processing. New York : Institute of Electrical and Electronics Engineers.
10. Godsill, S. Yang, L. (2006) Bayesian inference for continuous-time ar models driven by non-gaussian lévy processes. Proc. Int. Conf. Acoustics, Speech and Signal Processing. New York : Institute of Electrical and Electronics Engineers.
11. Grubmüller, H. Tavan, P. (1994) Molecular dynamics of conformational substates for a simplified protein model. J. Chem. Phys., 101, 5047 5057.
12. Hummer, G. (2005) Position-dependent diffusion coefficients and free energies from bayesian analysis of equilibrium and replica molecular dynamics simulations. New J. Phys., 7, no. 34.
13. Kalman, R. E. (1960) A new approach to linear filtering and prediction problems. J. Bas. Engng, 82, 35 45.
14. Kloeden, P. E. Platen, E. (1992) Numerical Solutions of Stochastic Differential Equations. New York : Springer.
15. Kramers, H. A. (1940) Brownian motion in a field of force and the diffusion model of chemical reactions. Physica, 7, 284 304.
16. Lasota, A. Mackey, M. C. (1994) Chaos, Fractals and Noise. New York : Springer.
17. Liu, J. S. (2001) Monte Carlo Strategies in Scientific Computing. New York : Springer.
18. Meng, X.-L. van Dyk, D. (1997) The EM algorithm - an old folk-song sung to a fast new tune (with discussion). J. R. Statist. Soc. B, 59, 511 567.
19. Nualart, D. (1991) The Malliavin Calculus and Related Topics. New York : Springer.
20. Øksendal, B. (2000) Stochastic Differential Equations, an Introduction with Applications. New York : Springer.
21. Pokern, Y. (2007) Fitting stochastic differential equations to molecular dynamics data. PhD Thesis. University of Warwick, Coventry.
22. Robert, C. P. Casella, G. (1999) Monte Carlo Statistical Methods. New York : Springer.
23. Roberts, G. O. Stramer, O. (2001) On inference for nonlinear diffusion models using the hastings-metropolis algorithms. Biometrika, 88, 603 621.
24. Roberts, G. O. Tweedie, R. L. (1997) Exponential convergence of langevin diffusions and their discrete approximations. Bernoulli, 2, 341 363.
25. Schlick, T. (2000) Molecular Modeling and Simulation - an Interdisciplinary Guide. New York : Springer.