用证据做决定

C. Jenkins
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引用次数: 0

摘要

贝叶斯证据比率提供了一种非常有吸引力的比较模型的方法,能够引用特定模型的概率似乎是做出选择的一个非常明确的动机。杰弗里斯证据尺度常用于解释证据比率。一个自然的问题是,当你根据证据比率的某些阈值进行选择时,你能有多少次做出正确的选择?证据比率在不同的数据实现中会有所不同,它的效用可以用类似于内曼-皮尔逊的方式来检验,看看统计能力(“正确”的机会)与假警报率之间的权衡是什么,当零实际上是真的时选择替代假设。我将展示一些简单的例子,这些例子表明,在不同的数据实现下,证据比率的范围可能会大得惊人。当必须做出决定时,最好不要简单地依赖杰弗里的量表,而且要检查做出“错误”决定的概率,如果某些证据比例被认为是决定性的。有趣的是,图灵知道这一点,并在二战期间应用了它,尽管(像其他很多东西一样)他没有发表它。
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Using evidence to make decisions
Bayesian evidence ratios give a very attractive way of comparing models, and being able to quote the odds on a particular model seems a very clear motivation for making a choice. Jeffreys' scale of evidence is often used in the interpretation of evidence ratios. A natural question is, how often will you get it right when you choose on the basis of some threshold value of the evidence ratio? The evidence ratio will be different in different realizations of the data, and its utility can be examined in a Neyman-Pearson like way to see what the trade-offs are between statistical power (the chance of ``getting it right'') versus the false alarm rate, picking the alternative hypothesis when the null is actually true. I will show some simple examples which show that there can be a surprisingly large range for an evidence ratio under different realizations of the data. It seems best not to simply rely on Jeffrey's scale when decisions have to be taken, but also to examine the probability of taking the ``wrong'' decision if some evidence ratio is taken to be decisive. Interestingly, Turing knew this and applied it during WWII, although (like much else) he did not publish it.
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