Abstract
Let Pe (S) denote the Bayes risk (probability of error) in testing two equally likely hypotheses H 0 versus H 1 using measurements in S, a subset of the set of possible measurements.
The possible values of Pe (S) as a function of S are considered. It has been shown that all orderings on Pe (S), satisfying the natural monotonicity constraint S′ ⊂ S ⇒ Pe (S′) ≥ Pe (S) can occur. We show that no other restrictions exist on the numbers Pe (S), 0 < Pe (S) ≤ ½, thus extending the known result from the achievability of orderings to the achievability of numerically specified sequences. Thus nonexhaustive (suboptimal) measurement-selection algorithms can be arbitrarily bad.