26. The method of claim 13 wherein said step of calculating a value for said class-other probability of correct classification from results obtained from said classification of patterns from said class-of-interest and said input-data-set using said adaptive Bayes classifier and said calculated class-of-interest a priori probability includes a step of calculating said value of class-other probability of correct classification, PCC C other , using the expression PCC C other = 1 ( PCC C int - 1 ) ⁡ [ PC C int + P C int ⁡ ( 1 - PCC C int ) - 1 ] .
13. A computer implemented method for estimating an a priori probability of a class-of-interest in an input-data-set and for estimating a classification error for an adaptive Bayes classifier in classifying unlabeled patterns from an input-data-set into two classes, a class-of-interest or a class-other, comprising the steps of: a computer to perform; receiving a training set of patterns from said class-of-interest, a set of unlabeled patterns from said input-data-set, and a plurality of predetermined of class-of-interest weights with each said class-weight having different predetermined values; and selecting a predetermined number of Gaussian kernel densities functions; and selecting parameter values for said Gaussian kernel densities functions where said selected parameter values cause said Gaussian kernel densities to approximate an unknown input-data-set probability density function; and executing a training stage using first of said class-of-interest weights, said training set of patterns from said class-of-interest, and said unlabeled patterns from said input-data-set, including a step of least squares approximation of a weighted class-of-interest posterior probability function using a linear combination of weighted said Gaussian kernel density functions, with said training stage repeated to provide said weighted class-of-interest posterior probability functions for each of the remaining said class-of-interest weights; and classifying said patterns from said class-of-interest and said input-data-set into two classes, said class-of-interest or said class-other, in accordance with a conditional test defined by an adaptive Bayes decision rule using first of said weighted class-of-interest posterior probability functions, with said classification repeated using said conditional test defined by said adaptive Bayes decision rule for all remaining said weighted class-of-interest posterior probability functions; and minimizing a least squares criteria to find a plurality of values for class-other probabilities of correct classification that provide identical estimates of said class-of-interest a priori probability; and calculating a value for said class-of-interest a priori probability in said input-data-set using one of said values of said class-other probabilities of correct classification that minimized said least squares criteria, and classifying said patterns from said class-of-interest and said input-data-set into two classes, said class-of-interest or said class-other, using said calculated value of said class-of-interest a priori probability and said conditional test defined by said adaptive Bayes decision rule; and calculating a value for said class-other probability of correct classification from results obtained from said classification of patterns from said class-of-interest and said input-data-set into two classes, said class-of-interest or said class-other, using said conditional test defined by said adaptive Bayes decision rule and said calculated class-of-interest a priori probability; and calculating a value for a probability of error for said adaptive Bayes classifier in classifying patterns from said input-data-set into two classes, said class-of-interest or said class-other, using said calculated value of said class-of-interest a priori probability and said calculated value of said class-other probability of correct classification; and wherein said class-of-interest a priori probability in said input-data-set is estimated and said probability of error for said adaptive Bayes classifier in classifying said input-data-set is estimated using only labeled patterns from said class-of-interest training set, and said unlabeled patterns from said input-data-set, and without any a priori knowledge of said class-other.