On a general relationship between estimation, detection, and the Bhattacharyya coefficient (Corresp.)

1 July 1969

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory

Vol. 15 (4) , 504-505
https://doi.org/10.1109/tit.1969.1054327

Abstract

A general and fundamental relationship between estimation, detection/pattern recognition, and the Bhattacharyya coefficient is established. Specifically, it is shown that a functional of the likelihood ratio necessary for Bayes optimal detection/pattern recognition is the Bayes-optimal mean-square estimate of the indicator variable\beta, where\beta = 1, 0, for hypothesesH_{1}, H_{0}, respectively. The Bhattacharyya coefficient is then shown to be the expected value of the estimation error standard deviation.

Keywords

This publication has 3 references indexed in Scilit:

Application of state variable techniques to optimal feature extraction
Proceedings of the IEEE, 1968
The Divergence and Bhattacharyya Distance Measures in Signal Selection
IEEE Transactions on Communications, 1967
Evaluation of likelihood functions for Gaussian signals
IEEE Transactions on Information Theory, 1965