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Biometrika 1983 70(1):175-181; doi:10.1093/biomet/70.1.175
© 1983 by Biometrika Trust
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Predictive inference, sufficiency, entropy and an asymptotic likelihood principle

WALLACE E. LARIMORE

Scientific Systems Inc., Cambridge, Massachusetts, U.S.A.

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.

Key Words: Akaike's criterion • Entropy • Foundations of statistics • Kullback-Leibler information • Likelihood • Predictive distribution • Predictive inference • Probability density estimation • Repeated sampling • Small sample • Sufficiency


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