Estimating functions of probability distributions from finite samples.

 
• Statement of the problem solved here
• Estimating from finite data is ubiquitous
• The distribution of data
• The Bayes' estimator
• The Bayes' estimator minimizes posterior mean square error
• Form of the prior
• Form of the integrals giving the estimator
• Integrating
• Estimators for the first and second moments of the entropy
• Entropy estimator comparison
• Estimators for moments, correlations, cumulants.
• Extended notation for more complicated functions of probability distributions
• More integration techniques
• Estimators for functions involving up-to-pairwise overlap integrals
• Multiple overlap integration