# Interpretations of Probability

> 【EN】Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means. —Bertrand Russell, 1929 Lecture (cited in Bell 1945, 587) One regularly reads and hears probabilistic claims like the following: The Democrats will probably win the next election. The coin is just as likely to land heads as tails. There’s a 30% chance of rain tomorrow. The probability that a radium atom decays in one year is roughly 0.0004. But what do these statements mean? This may be understood as a metaphysical question about what kinds of things are probabilities, or more generally as a question about what makes probability statements true or false. At a first pass, various interpretations of probability answer this question, one way or another. … 【中】词条以柯尔莫哥洛夫的概率演算为共同形式框架，提出解释的充分性标准，然后依次考察主要解释：古典概率、逻辑与证据概率、主观概率、频率解释、倾向解释与最佳系统解释。每种解释都要回答：概率是世界的客观特征，还是我们对世界的信念程度或证据关系。

- ID: m13281
- Category: decide
- Domain: 决策科学

## Definition

罗素曾打趣说，概率是现代科学中最重要的概念，却没人说得清它是什么意思。民主党可能会赢下届选举、明天降雨概率三成这类说法究竟在断言什么，是关于概率是什么、什么使命题为真的形而上学问题。 脚手架作用：- 数值澄清：先问概率指派给频率、倾向还是置信度，再决定如何取值。 - 方法择定：按解释选择统计工具，避免把频率结论硬套到单次事件上。

## How it works

概率演算只给出形式约束，即非负、归一与可加，并不规定语义。各解释的分歧在于把概率指派给什么：等可能事件的比例、证据间的逻辑关系、主体的置信度、长期频率、单次试验的客观倾向，或最佳系统定律中的模式。指派对象不同，同一个数值的意义就不同。

## Practice

1) 判定概率陈述出现的语境：单次事件、长期序列还是主观判断；2) 明确该语境下概率的指派对象；3) 检验所选解释能否同时容纳频率的稳定性与单次事件的可理解性；4) 避免在同一论证中偷换解释。

## Use

- 数值澄清：先问概率指派给频率、倾向还是置信度，再决定如何取值。 - 方法择定：按解释选择统计工具，避免把频率结论硬套到单次事件上。

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