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单词 Bayes Theorem
释义

Bayes Theorem

中文百科

贝叶斯定理 Bayes' theorem

（重定向自Bayes Theorem）
Un letrero de neón, mostrando el enunciado del teorema de Bayes
La visualización del teorema de Bayes por la superposición de dos árboles de decisión.
Tree diagram illustrating drug testing example. U, Ū,

贝叶斯定理（英语：Bayes' theorem）是概率论中的一个定理，它跟随机变量的条件概率以及边缘概率分布有关。在有些关于概率的解说中，贝叶斯定理（贝叶斯更新）能够告知我们如何利用新证据修改已有的看法。这个名称来自于托马斯·贝叶斯。

通常，事件A在事件B（发生）的条件下的概率，与事件B在事件A的条件下的概率是不一样的；然而，这两者是有确定的关系，贝叶斯定理就是这种关系的陈述。贝叶斯公式的用途在于通过己知三个概率函数推出第四个。它的内容是:在B出现的前提下,A出现的概率等于A和B都出现的概率乘以A出现的概率再除以B出现的概率。通过联系A与B,计算从一个事件产生另一事件的概率,即从结果上溯原。

英语百科

Bayes' theorem 贝叶斯定理

（重定向自Bayes Theorem）
A blue neon sign, showing the simple statement of Bayes' theorem
Visualization of Bayes' theorem by the superposition of two decision trees
Tree diagram illustrating drug testing example. U, Ū,
A geometric visualisation of Bayes' theorem. In the table, the values w, x, y and z give the relative weights of each corresponding condition and case. The figures denote the cells of the table involved in each metric, the probability being the fraction of each figure that is shaded. This shows that P (A |B ) P (B ) = P (B |A ) P (A ) i.e. P (A |B ) = P (B |A ) P (A )/P (B ) . Similar reasoning can be used to show that P (Ā|B ) = P (B |Ā) P (Ā)/P (B ) and so forth.

In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) describes the probability of an event, based on conditions that might be related to the event. For example, suppose one is interested in whether a person has cancer, and knows the person's age. If cancer is related to age, then, using Bayes' theorem, information about the person's age can be used to more accurately assess the probability that they have cancer.
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更新时间：2025/6/19 9:33:55