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

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 hypotheses H_{1}, H_{0} , respectively. The Bhattacharyya coefficient is then shown to be the expected value of the estimation error standard deviation.