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OCIAM**

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Oxford Centre for Industrial and Applied Mathematics
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Dr Leonard A Smith's Publications**

Indistinguishable States I :
The Perfect Model Scenario

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

ABSTRACT
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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