亨普尔乌鸦悖论的nonBayesian观点
A nonBayesian view of Hempel's paradox of the ravens
摘要：
在亨佩尔的乌鸦悖论中，看到一支红铅笔被认为是所有乌鸦都是黑色的证据。也被称为证实的悖论，悖论及其许多解决方案表明，我们不能低估在评估支持假设的证据时所需的逻辑和统计要素。以前对悖论的分析大多是在贝叶斯框架内进行的。这些分析和亨佩尔本人普遍接受的矛盾的结论;它感觉自相矛盾的推测，因为证据的数量是非常小的。在这里，我描述了一个非贝叶斯分析的各种统计模型，伴随着基于似然推理。分析表明，悖论感觉自相矛盾，因为有自然的模型，观察红色铅笔与乌鸦的颜色无关。一般而言，证据的价值主要取决于抽样方案和有关模型基本参数的假设。
英文摘要：
In Hempel's paradox of the ravens, seeing a red pencil is considered as supporting evidence that all ravens are black. Also known as the Paradox of Confirmation, the paradox and its many resolutions indicate that we cannot underestimate the logical and statistical elements needed in the assessment of evidence in support of a hypothesis. Most of the previous analyses of the paradox are within the Bayesian framework. These analyses and Hempel himself generally accept the paradoxical conclusion; it feels paradoxical supposedly because the amount of evidence is extremely small. Here I describe a nonBayesian analysis of various statistical models with an accompanying likelihood-based reasoning. The analysis shows that the paradox feels paradoxical because there are natural models where observing a red pencil has no relevance to the color of ravens. In general the value of the evidence depends crucially on the sampling scheme and on the assumption about the underlying parameters of the relevant model.
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