LA-UR, Vol. 92, No. 4369, 1992

David H. Wolpert, David R. Wolf
 
 

Abstract:

This paper is the first of two on the problem of estimating a function of a probability distribution from a finite set of samples of that distribution. In this paper a bayesian analysis of this problem is presented, the optimal properties of the Bayes estimators are discussed, and as an example of the formalism, closed form expressions for the Bayes estimators for the moments of the Shannon entropy function are derived. Numerical results are presented that compare the Bayes estimator to the frequency counts estimator for the Shannon entropy.
 
 

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