Oxford Centre for Industrial and Applied Mathematics

Dr Leonard A Smith's Publications

K. Judd and L.A. Smith (2001) Physica D 151, 125--141.


An accurate forecast of a nonlinear system is often thought to require an accurate estimation of the initial state. It is shown that even under the ideal conditions of a perfect model and infinite past observations of a deterministic nonlinear system, uncertainty in the observations makes exact state estimation is impossible; one can only obtain 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.

Contact Information

Tel: 01865-2-70517
E-mail: lenny@maths.ox.ac.uk

Last updated: 14 Feb 2001

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