论文标题

从统计角度来看,Popper的伪造和佐证

Popper's falsification and corroboration from the statistical perspectives

论文作者

Lee, Youngjo, Pawitan, Yudi

论文摘要

概率的作用似乎是不确定性的关键衡量标准,它用于经验科学的实际诱导。然而,波普尔在拒绝归纳概率和假设的逻辑概率方面是强调的。此外,对他而言,佐证的程度不可能是概率。取而代之的是,他提出了一种演绎测试方法。在许多方面,这种辩证法的张力在统计数据中具有许多相似之处,而贝叶斯人在逻辑感应方面与非bayesians或另一侧的非bay徒或常见者。简单地说,Popper似乎处于频繁的一面,但是在非bayesian方面的最新合成可能会将Popperian视图引导到更细微的目的地。逻辑概率似乎非常适合衡量部分证据或支持,那么如果我们拒绝它,我们可以使用什么?在过去的100年中,统计学家还建立了一个称为“可能性”的相关概念,该概念在统计建模和推理中发挥了核心作用。值得注意的是,这种不确定性概念在非统计文献中在很大程度上是未知的或至少被严重低估了。作为佐证的衡量标准,可能性满足了Popperian的要求,即这不是概率。我们的目的是通过讨论两个众所周知的逻辑谬误来介绍可能性及其最近的扩展,以强调其缺乏认可可能导致我们在伪造和证实假设的论述中引起了不必要的困惑。我们强调了100年的可能性概念的发展。 2021年将标志着可能性100周年,因此,我们希望它能长寿,并增加对非统计文献的欣赏。

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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