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September 2002 A Mathematical Framework for Quantifying Predictability Through Relative Entropy
David Cai, Richard Kleeman, Andrew Majda
Methods Appl. Anal. 9(3): 425-444 (September 2002).

Abstract

Kleeman has recently demonstrated that the relative entropy provides a significant measure of the information content of a prediction ensemble compared with the climate record in several simplified climate models. Here several additional aspects of utilizing the relative entropy for predictability theory are developed with full mathematical rigor in a systematic fashion which the authors believe will be very useful in practical problems with many degrees of freedom in atmosphere/ocean and biological science. The results developed here include a generalized signal-dispersion decomposition, rigorous explicit lower bound estimators for information content, and rigorous lower bound estimates on relative entropy for many variables, N, through N, one-dimensional relative entropies and N, two-dimensional mutual information functions. These last results provide a practical context for rapid evaluation of the predictive information content in a large number of variables.

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David Cai. Richard Kleeman. Andrew Majda. "A Mathematical Framework for Quantifying Predictability Through Relative Entropy." Methods Appl. Anal. 9 (3) 425 - 444, September 2002.

Information

Published: September 2002
First available in Project Euclid: 17 June 2005

zbMATH: 1084.94010
MathSciNet: MR2023134

Rights: Copyright © 2002 International Press of Boston

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Vol.9 • No. 3 • September 2002
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