Indistinguishable states I. Perfect model scenario

被引:56
作者
Judd, K [1 ]
Smith, L
机构
[1] Univ Western Australia, Ctr Appl Dynam & Optimizat, Dept Math & Stat, Perth, WA 6907, Australia
[2] Oxford Ctr Ind & Appl Math, Math Inst, Oxford, England
[3] Univ London London Sch Econ & Polit Sci, Ctr Anal Time Series, Dept Stat, London WC2A 2AE, England
来源
PHYSICA D | 2001年 / 151卷 / 2-4期
基金
澳大利亚研究理事会;
关键词
indistinguishable state; perfect model scenario; nonlinear system; ensemble forecasting;
D O I
10.1016/S0167-2789(01)00225-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
An accurate forecast of a nonlinear system will require an accurate estimation of the initial state. It is shown that even under the ideal conditions of a pet-feet model and infinite past observations of a deterministic nonlinear system, uncertainty in the observations makes exact state estimation is impossible. Consistent with the noisy observations there is a set of states indistinguishable from the true state. This implies that an accurate forecast must be based on a probability density on the indistinguishable states. This paper shows that this density can be calculated by first calculating a maximum likelihood estimate of the state, and then an ensemble estimate of the density of states that are indistinguishable from the maximum likelihood state. A new method for calculating the maximum likelihood estimate of the true state is presented which allows practical ensemble forecasting even when the recurrence time of the system is long. In a subsequent paper the theory and practice described in this paper are extended to an imperfect model scenario. (C) 2001 Published by Elsevier Science B.V.
引用
收藏
页码:125 / 141
页数:17
相关论文
共 36 条
[1]  
[Anonymous], 1981, LECT NOTES MATH
[2]   LIKELIHOOD AND BAYESIAN PREDICTION OF CHAOTIC SYSTEMS [J].
BERLINER, LM .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1991, 86 (416) :938-952
[3]  
Boender C. G. E., 1995, HDB GLOBAL OPTIMIZAT, V2, P829
[4]   STATE-SPACE RECONSTRUCTION IN THE PRESENCE OF NOISE [J].
CASDAGLI, M ;
EUBANK, S ;
FARMER, JD ;
GIBSON, J .
PHYSICA D-NONLINEAR PHENOMENA, 1991, 51 (1-3) :52-98
[5]  
COUTIER P, 1997, J METEOROLOGY SOC JA, V75, P211
[6]  
Daley R., 1991, Atmospheric data analysis
[7]  
DAVIES M, 1994, PHYSICA D, V79, P174
[8]  
Guckenheimer J., 1983, NONLINEAR OSCILLATIO, V42
[9]   A NOISE-REDUCTION METHOD FOR CHAOTIC SYSTEMS [J].
HAMMEL, SM .
PHYSICS LETTERS A, 1990, 148 (8-9) :421-428
[10]  
Hansen JA, 2000, J ATMOS SCI, V57, P2859, DOI 10.1175/1520-0469(2000)057<2859:TROOCI>2.0.CO