The numerical measure of the success of predictions.
The numerical measure of the success of predictions.
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DOI：
10.1126/science.ns-4.93.453-a
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发表时间：
1884-11-14
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影响因子：
--
通讯作者：
Peirce, C S
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作者：
Peirce, C S
假设我们有一种方法，通过这种方法，提出了两种选择，可以在任何情况下回答特定类型的问题，尽管并不总是正确的。此外，假设大量这样的答案已经与事件对照地列出，从而我们给出了以下四个数字：-(Aa)，答案是第一种方法，事件是第一种方法的问题的数目；(Ab)‘，答案是第一种方法，事件是第二种方法的问题的数目；(BA)，答案是第二种方法，事件是第一种方法的问题的数量·(Bb)，答案是第二种方法，事件是第二种方法的问题的数量。然后，问题是，从这些数据中，给产生答案的方法的成功或科学性分配一个数字度量。GK Gilbert先生(美国1网络气象杂志，1884年9月)最近提出了一个用于这一目的的公式；我想提供另一个公式。我利用了两个原则。第一种是，任何两种方法都被认为是完全知识的相等近似，从长远来看，这将给出(Aa)、(Ab)、(Ba)和(Bb)相同的值。第二个原则是，如果答案是通过随机选择一定比例的问题获得的，由一个绝对可靠的证人回答，而其余的问题是由一个完全无知的人随机回答的(使用是和否，即确定相对频率)，那么这样获得的答案的接近程度将通过向绝对可靠的证人提出问题的比例来衡量。第二个证人可能知道他应该回答‘是’的频率；但我不相信他，因为他在应该回答的时候是无知的，是的。
Suppose we have a method by which questions of a certain kind, presenting two alternatives, can in every case be answered, though not always rightly. Suppose, further, that a large number of such answers have been tabulated in conlparison with the events, so that we have given the following four numbers:-(aa), the nurnber of questions for which the answers were the first way and the events the first way;(ab)', the number of questions for which the answers were the first way and the events the second way;(ba), the number of questions for wbich the answers were the second way and the events the first way·(bb), the~ umber of questions for which the answers were the second way and the events the second wa~.Then the problem is, frorn these data to assign a numerical measure to the success or science of the method by which the answers have been produced. Mr. GK Gilbert (A1ner. 1neteorologicaljournal, Sep-tember, 1884) has recently proposed a formula for this purpose; and I desire to offer another. I make use of two principles. The first is, that any two rnethods are to be regarded as equal approximations to complete knowledge, which, in the long-run, would give the same values for (aa),(ab),(ba), and (bb). The second principle is, that if the answers had been obtained by selecting a determinate proportion of the questions by chance, to be answered by an infallible witness, while the rest were answered hy an utterly ignorant person at random (using yes and no, vith determinate relative frequencies), then the approxinlation to kno,,'ledge in the answers so obtained would be measured by the fraction expressing the proportion of questions put to the infallible witness. The second witness may know how often he ought to answer'yes;'but I give him no credit for that, because he is ignorant when he ought to answer, yes.'