prior 和 priori的区别

看到MAP的全称，Maximum a Posteriori想到这个问题，基本上书上说的都是prior，posterior

但是偶尔也有priori和posteriori的说法。

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以下内容来自维基百科：https://en.wikipedia.org/wiki/A_priori_and_a_posteriori

priori和posteriori是哲学术语，并不是Beyes推理里的先验后验。

priori knowledge表示只由逻辑和重言式推理能得到的知识；

posteriori knowledge表示依赖“经验”的知识；

有个例子：

A priori

Consider the proposition, "If George V reigned at least four days, then he reigned more than three days." This is something that one knows a priori, because it expresses a statement that one can derive by reason alone.

A posteriori

Compare this with the proposition expressed by the sentence, "George V reigned from 1910 to 1936." This is something that (if true) one must come to know a posteriori, because it expresses an empirical fact unknowable by reason alone.

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还有一个词：priori probability，或者a priori prior，一般表示uninformative prior或者objective prior，是先验的一种，priori一词和prior先验没有关系

见 https://en.wikipedia.org/wiki/Prior_probability

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posteriori一词也不是指posteriori：

“The phrase a-posteriori probability is also used as an alternative to empirical probability”，经验分布和后验没有任何关系，对应于priori probability。

“用这个词来指代经验分布是历史原因”，但是，beyesian推理中，“偶尔”(MAP)用a-posteriori来表示posterior(后验).

见 https://en.wikipedia.org/wiki/Empirical_probability

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总结一下，

prior：先验

posterior：后验

priori：priori probability——和经验无关的，逻辑得出的概率。priori prior——uninformative prior

posteriori：a-posteriori probability——经验分布，和priori对应；“偶尔”指代posterior(后验)