Abstract :
An important measure concerning the use of statistical decision schemes is the error probability associated with the decision rule. Several methods giving bounds on the error probability are presently available, but, most often, the bounds are loose. Those methods generally make use of so-cailed distances between statistical distributions. In this paper a new distance is proposed which permits tighter bounds to be set on the error probability of the Bayesian decision rule and which is shown to be closely related to several certainty or separability measures. Among these are the nearest neighbor error rate and the average conditional quadratic entropy of Vajda. Moreover, our distance bears much resemblance to the information theoretic concept of equivocation. This relationship is discussed. Comparison is made between the bounds on the Bayes risk obtained with the Bhattacharyya coefficient, the equivocation, and the new measure which we have named the Bayesian distance.
Keywords :
Bayesian decision rule, Bhattacharyya coefficient, bounds on error probability, conditional entropy, error probability, nearest neighbor error rate, pattern recognition, quadratic entropy, separability measure.; Bayesian methods; Control systems; Entropy; Error analysis; Error probability; Nearest neighbor searches; Pattern recognition; Statistical distributions; Testing; Uncertainty; Bayesian decision rule, Bhattacharyya coefficient, bounds on error probability, conditional entropy, error probability, nearest neighbor error rate, pattern recognition, quadratic entropy, separability measure.;
