Accession Number : AD0822907

Title :   COMPOUND BAYES LEARNING WITHOUT A TEACHER.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CA STANFORD ELECTRONICS LABS

Personal Author(s) : Alens, Normonds

Report Date : AUG 1967

Pagination or Media Count : 131

Abstract : The compound decision problem and the empirical Bayes problem are considered. The underlying probability densities of the unlabeled samples are specified as belonging only to a family of probability density functions. Under assumptions of identifiability and some regularity conditions, the unknown probability density functions and the frequencies of the samples are estimated from the received samples. Based on these estimates, a compound decision procedure is exhibited such that the upper bound of the difference between the risk corresponding to the compound rule and the component Bayes risk on the empirical prior probabilities converges to zero. Rates of convergence of the upper bound to zero are given for the empirical Bayes problem. In the empirical Bayes problem a nonparametric estimation is considered and, under certain assumptions, a decision rule is exhibited such that the corresponding risk converges to the optimal Bayes risk. Rates of convergence are given. (Author)

Descriptors :   *DECISION MAKING), *INFORMATION THEORY), (*PROBLEM SOLVING, (*TEACHING METHODS, RANDOM VARIABLES, MATHEMATICAL PREDICTION, LEARNING, SEQUENTIAL ANALYSIS, PATTERN RECOGNITION, PROBABILITY DENSITY FUNCTIONS, FUNCTIONAL ANALYSIS, DISTRIBUTION THEORY.

Subject Categories : Information Science
      Humanities and History
      Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE