从统计学角度看波普尔的证伪与确证
Popper's falsification and corroboration from the statistical perspectives
摘要：
概率作为不确定性的关键度量，在经验科学的实践归纳中被用作其他工具，其作用似乎无可争议。然而，波普尔在他拒绝归纳概率和假设的逻辑概率方面是谨慎的;此外，对他来说，确证的程度不能是概率。相反，他提出了一种演绎的测试方法。在许多方面，这种辩证的紧张关系在统计学中有许多相似之处，贝叶斯主义者站在逻辑归纳的一边，而非贝叶斯主义者或频率主义者站在另一边。简单地说，波普尔似乎是站在频率论一边的，但最近对非贝叶斯观点的综合可能会将波普尔的观点引向一个更微妙的目的地。逻辑概率似乎非常适合于衡量部分证据或支持，那么如果我们要拒绝它，我们可以使用什么呢？在过去的100年里，统计学家还发展了一个相关的概念，称为似然，它在统计建模和推断中发挥了核心作用。值得注意的是，这种费雪式的不确定性概念在很大程度上是未知的，或者至少在非统计文献中被严重低估。作为确证的一种度量，似然满足波普尔的要求，即它不是概率。我们的目的是通过讨论两个著名的逻辑谬误来介绍可能性及其最近的扩展，以强调它的缺乏认识可能导致了我们关于证伪和确证假设的话语中不必要的混乱。我们强调了可能性概念100年的发展。2021年将是可能性的100周年纪念，因此我们希望这篇论文能够长寿，并在非统计文献中获得更多的赞赏。
英文摘要：
The role of probability appears unchallenged as the key measure of uncertainty, used among other things for practical induction in the empirical sciences. Yet, Popper was emphatic in his rejection of inductive probability and of the logical probability of hypotheses; furthermore, for him, the degree of corroboration cannot be a probability. Instead he proposed a deductive method of testing. In many ways this dialectic tension has many parallels in statistics, with the Bayesians on logico-inductive side vs the non-Bayesians or the frequentists on the other side. Simplistically Popper seems to be on the frequentist side, but recent synthesis on the non-Bayesian side might direct the Popperian views to a more nuanced destination. Logical probability seems perfectly suited to measure partial evidence or support, so what can we use if we are to reject it? For the past 100 years, statisticians have also developed a related concept called likelihood, which has played a central role in statistical modelling and inference. Remarkably, this Fisherian concept of uncertainty is largely unknown or at least severely under-appreciated in non-statistical literature. As a measure of corroboration, the likelihood satisfies the Popperian requirement that it is not a probability. Our aim is to introduce the likelihood and its recent extension via a discussion of two well-known logical fallacies in order to highlight that its lack of recognition may have led to unnecessary confusion in our discourse about falsification and corroboration of hypotheses. We highlight the 100 years of development of likelihood concepts. The year 2021 will mark the 100-year anniversary of the likelihood, so with this paper we wish it a long life and increased appreciation in non-statistical literature.
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