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Predictive Inference, Sufficiency, Entropy and an Asymptotic Likelihood Principle

Wallace E. Larimore
Biometrika
Vol. 70, No. 1 (Apr., 1983), pp. 175-181
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2335955
Stable URL: http://www.jstor.org/stable/2335955
Page Count: 7
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Predictive Inference, Sufficiency, Entropy and an Asymptotic Likelihood Principle
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Abstract

The objective of inferring stochastic models from a set of data is to obtain the best description, by using a probability model, of the statistical behaviour of future samples of the process. A conceptual repeated sampling experiment is considered for evaluating a predictive distribution used to describe such future observations and leads to an asymptotic likelihood principle. Considerations of likelihood and sufficiency lead to the use of entropy or the Kullback-Leibler information as the natural measure of approximation to the actual distribution by a predictive distribution in repeated samples. This gives a small-sample justification for the use of entropy for evaluating parameter estimation as well as model order and structure determination procedures.

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