Estimating Functions of Probability Distributions from a Finite Set of Samples, Part 1: Bayes Estimators and the Shannon Entropy

摘要

We present estimators for entropy and other functions of a discreteprobability distribution when the data is a finite sample drawn from thatprobability distribution. In particular, for the case when the probabilitydistribution is a joint distribution, we present finite sample estimators forthe mutual information, covariance, and chi-squared functions of thatprobability distribution.