论文标题
使用证据做出决定
Using evidence to make decisions
论文作者
论文摘要
贝叶斯证据比率提供了一种非常有吸引力的模型方式，并且能够在特定模型上引用赔率似乎是做出选择的非常清晰的动机。 Jeffreys的证据规模通常用于证据比率的解释。一个自然的问题是，当您根据证据比率的某种阈值值选择时，您将多久正确地获得一次正确的问题？在数据的不同实现中，证据比将有所不同，并且可以在Neyman-Pearson喜欢的方式中检查其效用，以查看统计能力之间的权衡（``将其正确''的机会）与虚假警报率相比，在null实际上是真实的时选择替代假设。我将显示一些简单的示例，这些示例表明，在数据的不同实现下，证据比率可能存在很大的范围。最好是在必须做出决定时仅仅依靠杰弗里的规模，而且还要检查如果认为某些证据比是决定性的，则可以检查做出``错误''决定的可能性。有趣的是，图灵知道这一点，并在第二次世界大战期间应用了这一点，尽管他（与其他许多相同）他没有出版。
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.
