The arbitrary relation between probability of error and measurement subset
The arbitrary relation between probability of error and measurement subset
复制标题
误差概率与测量子集之间的任意关系
DOI：
10.1080/01621459.1980.10477438
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发表时间：
1980
影响因子：
3.7
通讯作者：
J. V. Campenhout
中科院分区：
文献类型：
--
作者：
J. V. Campenhout
设Pe（S）表示用S中的测量值检验两个可能性相等的假设H 0与H1时的贝叶斯风险（错误概率），S是可能测量值集的一个子集.考虑了Pe（S）作为S的函数的可能值。证明了Pe（S）上满足自然单调性约束S′ <$S <$Pe（S′）≥ Pe（S）的所有序都可能出现.我们证明了对Pe（S），0 < Pe（S）≤ 1/2不存在其他限制，从而将已知结果从序的可解性推广到数值指定序列的可解性.因此，非穷举（次优）测量选择算法可以是任意坏的。
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.