On the problem of the most efficient tests of statistical hypotheses
On the problem of the most efficient tests of statistical hypotheses
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DOI：
10.1098/rsta.1933.0009
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发表时间：
1933-03-01
影响因子：
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通讯作者：
Neyman, J
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文献类型：
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作者：
Neyman, J
检验统计假设的问题由来已久。它的起源通常与托马斯·贝叶斯（Thomas Bayes）的名字联系在一起，他提出了关于给定事件的可能“原因”的概率后验的著名定理。从那以后，许多作家都讨论过这个问题，我们在这里只提到两位，伯特兰和博雷尔，他们的不同观点很好地说明了我们将要探讨这个问题的观点。贝特朗以统计的形式提出了各种各样的假设，例如，假设从地球上看，一组给定的恒星之间的角距离相对较小，它们在太空中形成了一个“系统”或群体。他的攻击方法，也就是通常使用的方法，主要是计算概率P，即如果检验的假设为真，观察到的事实中出现某种特征x的概率P。如果P非常小，这通常会被认为表明假设H可能是错误的，反之亦然。伯特兰悲观地认为，这种测试不可能给出可靠的结果。然而，在后来的讨论中，Borel认为所描述的方法可以成功地应用，只要观察到的事实的特征x被适当地选择——事实上，是他称之为“en quelque sorte remarquable”的特征。
The problem of testing statistical hypotheses is an old one. Its origin is usually connected with the name of Thomas Bayes, who gave the well-known theorem on the probabilities aposterioriof the possible “causes" of a given event. Since then it has been discussed by many writers of whom we shall here mention two only, Bertrand and Borel, whose differing views serve well to illustrate the point from which we shall approach the subject. Bertrand put into statistical form a variety of hypotheses, as for example the hypothesis that a given group of stars with relatively small angular distances between them as seen from the earth, form a “system” or group in space. His method of attack, which is that in common use, consisted essentially in calculating the probability, P, that a certain character,x, of the observed facts would arise if the hypothesis tested were true. If P were very small, this would generally be considered as an indication that the hypothesis, H, was probably false, andvice versa. Bertrand expressed the pessimistic view that no test of this kind could give reliable results. Borel, however, in a later discussion, considered that the method described could be applied with success provided that the character,x, of the observed facts were properly chosen—were, in fact, a character which he terms “en quelque sorte remarquable.”