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Under the truncated procedure, the process must terminate in at most N stages. Truncation is a compromise between an entirely sequential procedure and a classical, fixed-sample decision procedure as Eq. 8). I t is an attempt to reconcile the good properties of both procedures: (1) the sequential property of examining measurements as they accumulate, and (2) the classical property of guaranteeing that the tolerances will be met with a specified number of available measurements. 111. Forward Sequential Classification Procedure with Time-Varying Stopping Boundaries As described in Section 11, the error probabilities eii can be prespecified in SPKT and GSPRT.

From Eqs. 5), the condition is equivalent to the condition P(. I B) V ) > P(. 8) P(8), this means that in our > ~ ( I x8); otherwise decide 8. Inspection of Fig. 9. T h u s it happens that we have come full circle and have returned to our original, intuitively suggested decision rule. Now, however, we have a theoretical justification for this rule, and we have a much more general approach for deriving decision rules, the method of statistical decision theory. D. Improving the Feature Extractor Unfortunately, the major practical result of our attempt to improve the classifier was a demonstration that it was doing about as well as can be expected.

FU It is noted from Eq. , m(i # j ) [Nilsson, 19651. 16) Eq. 16) is, in general, a hyperquadric. If 2% = ZJ = Z, Eq. 17) which is a hyperplane. It is noted from Eq. 8) that the Bayes’ decision rule with (0, 1) loss function is also the unconditional maximum-likelihood decision rule. Furthermore, the (conditional) maximum-likelihood decision may be regarded as the Bayes’ decision rule, Eq. , m. I n the statistical classification systems described above, all the N features are observed by the classifier at one stage.

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