如何从现有的条件概率表中创建联合概率表? (CPT) [英] How to create a joint probability table from existing conditioinal probability tables? (CPTs)

问题描述

我有下表，其相关性如下:

I have the following tables ,with the dependencies below :

我想为P(M,P,W,B)创建一个联合概率表，它看起来像这样(当然，您可以假设未向我提供下表 ，从这个问题的答案):

And I want to create the joint-probability table for P(M,P,W,B) , which looks like this (and of course ,you can assume that the below table is not given to me , it is taken from the answer for this question) :

有人可以解释一下如何为P(M,P,W,B)创建联合概率表吗?

Can someone please explain how can I create the joint probability table for P(M,P,W,B) ?

非常感谢

推荐答案

P(M，P，W，B)的联合概率仅仅是其他表中各项的乘积.这来自维基百科:

The joint probability for P(M,P,W,B) is simply the product of the entries of the other tables. This is from Wikipedia:

X 是关于 G 的贝叶斯网络，则可以将其联合概率密度函数(相对于乘积度量)写成单个密度的乘积函数，取决于其父变量:

X is a Bayesian network with respect to G if its joint probability density function (with respect to a product measure) can be written as a product of the individual density functions, conditional on their parent variables:

其中 pa(v)是 v 的父级集合(即，通过单个边直接指向 v 的那些顶点).

where pa(v) is the set of parents of v (i.e. those vertices pointing directly to v via a single edge).

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