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.