更新概率
Updating Probabilities
摘要：
正如Monty Hall难题这样的例子所显示的那样，应用条件作用来更新“朴素空间”上的概率分布，而不考虑所使用的协议，往往会导致违反直觉的结果。在这里，我们研究为什么。在统计学文献中，一个被称为CAR（“随机粗化”）的标准描述了在天真空间中“天真”条件作用的特征。我们表明，CAR条件持有，而不经常，我们提供了一个程序的特点，它，通过给一个随机算法，生成所有和唯一的分布，CAR持有。这基本上扩展了先前对CAR的表征。我们还考虑更广义的更新概念，如杰弗里条件和最小化相对熵（MRE）。我们给出了一个概括的CAR条件的特点时，杰弗里条件导致适当的答案，并表明存在一些非常简单的设置中，MRE基本上从来没有给出正确的结果。这概括和互连以前的结果在CAR和MRE的文献中获得的。
英文摘要：
As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a ``naive space'', which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine why. A criterion known as CAR (``coarsening at random'') in the statistical literature characterizes when ``naive'' conditioning in a naive space works. We show that the CAR condition holds rather infrequently, and we provide a procedural characterization of it, by giving a randomized algorithm that generates all and only distributions for which CAR holds. This substantially extends previous characterizations of CAR. We also consider more generalized notions of update such as Jeffrey conditioning and minimizing relative entropy (MRE). We give a generalization of the CAR condition that characterizes when Jeffrey conditioning leads to appropriate answers, and show that there exist some very simple settings in which MRE essentially never gives the right results. This generalizes and interconnects previous results obtained in the literature on CAR and MRE.
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