Indistinguishable states II the imperfect model scenario

Physica D: Nonlinear Phenomena

Volumn 196, Issue 3-4, 2004, Pages 224-242

  Judd, Kevin ^a   Smith, Leonard A ^b,c  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b LONDON SCHOOL OF ECONOMICS   (United Kingdom)

^c UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Forecasting; Imperfect models; Model; Noisy observations; Probability; Shadowing

Indexed keywords

ALGORITHMS; INFORMATION ANALYSIS; NONLINEAR SYSTEMS; PARAMETER ESTIMATION; PROBABILITY DISTRIBUTIONS; TRAJECTORIES;

IMPERFECT MODELS; MODEL; NOISY OBSERVATIONS; SHADOWING;

CHAOS THEORY;

EID: 4344580350     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2004.03.020     Document Type: Article

References (29)

1. K. Seven, On explanatory depth and predictive power, Hydrol. Process. 15 (2001) 3069-3072.
2. K. Beven, Towards a coherent philosophy for modelling the environment, Proc. Roy. Soc. A 458 (2002) 2465-2484.
3. N. Cartwright, How the Laws of Physics Lie, Oxford University Press, 1983.
4. R. Fitzgerald, Numerical Bayesian Methods Applied to Signal Processing, Springer, 1997.
5. A.C. Fowler, M.C. Mackey, Relaxation oscillations in a class of delay differential equations, SIAM J. Appl. Math. 63 (1) (2002) 299-323.
6. J.A. Hansen, L.A. Smith, The role of operational constraints in selecting supplementary observations, J. Atmos. Sci. 57 (17) (2000) 2859-2871.
7. K. Ikeda, Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system, Opt. Commun. 30 (1979) 257.
8. K. Judd, A.I. Mees, Embedding as a modeling problem, Physica D 120 (1998) 273-286.
9. K. Judd, M. Small, Towards long-term prediction, Physica D 136 (1999) 31-44.
10. K. Judd, L.A. Smith, Indistinguishable states I, Physica D 151 (2001) 125.
11. K. Judd, L.A. Smith, Gradient free descent, Physica D 190 (2004) 153-166.
12. W. Just, H. Kantz, C. Rodenbeck, M. Helm, Stochastic modelling: replacing fast degrees of freedom by noise, J. Phys. 34 (15) (2001) 3199-3213.
13. M.C. Kennedy, A. O'Hagan, Bayesian calibration of computer models, J. Roy. Stat. Soc. Ser. B 63 (2001) 425-464.
14. E.N. Lorenz, Predictability - a problem partly solved, in: Proceedings of the ECMWF Workshop on Predictability, vol. 1, Shinfield Park, Reading, UK, 1996 (ECMWF).
15. A.H. Murphy, R.L. Winkler, A general framework for forecast verification, Monthly Weather Rev. 115 (1987) 1330-1338.
16. E. Ott, Chaos in Dynamical Systems, CUP, Cambridge, 1993.
17. T.N. Palmer, R. Buizza, F. Molteni, Y.-C. Chen, S. Corti, Singular vectors and the predictability of weather and climate, Philos. Trans. R. Soc. Lond. A 348 (1688) (1994) 459-475.
18. T.N. Palmer, Predicting uncertainty in forecasts of weather and climate, Rep. Prog. Phys. 63 (2000) 71-116.
19. P.E. Rapp, T.I. Schmah, A.I. Mees, Models of knowing and the investigation of dynamical systems, Physica D 132 (1999) 133-149.
20. M.S. Roulston, L.A. Smith, Evaluating probabilistic forecasts using information theory, Monthly Weather Rev. 130 (6) (2002) 1653-1660.
21. D.B. Rubin, et al., Using the SIR algorithm to simulate posterior distributions, in: J. Bernardo (Ed.), Bayesian Statistics 3, Oxford Unversity Press, 1988.
22. L.A. Smith, Accountability and error in ensemble forecasting, in: Proceedings of the ECMWF Seminar on Predictability, vol. 1, Shinfield Park, Reading, 1995, pp. 351-369 (ECMWF).
23. L.A. Smith, The maintenance of uncertainty, in: Proceedings of the International School of Physics "Enrico Fermi", vol. CXXXIII, Bologna, Italy, 1997, pp. 177-246 (Societa Italiana di Fisica).
24. L.A. Smith, Disentangling uncertainty and error: on the predictability of nonlinear systems, in: Alistair I. Mees (Ed.), Nonlinear Dynamics and Statistics, Birkhauser, Boston, 2000, pp. 31-64.
25. L.A. Smith, Limits to predictability in 2000 and 2100, in: S. Haykin (Ed.), Proceedings of IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium, IEEE, Piscataway, 2000, pp. 129-134.
26. L.A. Smith, What might we learn from climate forecasts? Proc. Natl. Acad. Sci. 4 (99) (2002) 2487-2492.
27. L.A. Smith, C. Ziehmann-Schlumbohm, K. Fraedrich, Uncertainty dynamics and predictability in chaotic systems, Q. J. R. Meteorol. Soc. 125 (1999) 2855-2886.
28. J. Stark, D. Broomhead, M. Davies, J. Huke, Delay embeddings for forced systems, J. Nonlinear Sci. 13 (2003) 519-577.
29. R.L. Winker, A.H. Murphy, "Good" probability assessors, J. Appl. Meteor. 7 (1968) 751-758.