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==举例==
==举例==
[[Image:SimpleBayesNet.svg|400px|thumb|right|A simple Bayesian network with [[conditional probability table]]s ]]
[[Image:SimpleBayesNet.svg|400px|thumb|right|一个简单的贝叶斯网络，及其条件概率表 ]]
The joint probability function is:
The joint probability function is:
对应的联合概率函数是:
where G = "Grass wet (true/false)", S = "Sprinkler turned on (true/false)", and R = "Raining (true/false)".
where G = "Grass wet (true/false)", S = "Sprinkler turned on (true/false)", and R = "Raining (true/false)".
其中G表示“草地湿了(true/false)”，S表示“洒水器打开(true/false)”，R表示“下雨(true/false)”。
To answer an interventional question, such as "What is the probability that it would rain, given that we wet the grass?" the answer is governed by the post-intervention joint distribution function
To answer an interventional question, such as "What is the probability that it would rain, given that we wet the grass?" the answer is governed by the post-intervention joint distribution function
这个模型还回答干预性的问题，比如“现在我们把草弄湿了，那么下雨的可能性有多大? ”答案取决于干预后的'''<font color="#ff8000">联合分布函数 Joint distribution function</font>'''
: <math>\Pr(S,R\mid\text{do}(G=T)) = \Pr(S\mid R) \Pr(R)</math>
: <math>\Pr(S,R\mid\text{do}(G=T)) = \Pr(S\mid R) \Pr(R)</math>
obtained by removing the factor <math>\Pr(G\mid S,R)</math> from the pre-intervention distribution. The do operator forces the value of G to be true. The probability of rain is unaffected by the action:
obtained by removing the factor <math>\Pr(G\mid S,R)</math> from the pre-intervention distribution. The do operator forces the value of G to be true. The probability of rain is unaffected by the action:
该分布通过从干预前的分布中去除因子<math>\Pr(G\mid S,R)</math>得到，其中do算子强行使 G 的值为真。下雨的可能性不受行动的影响:
该分布通过从干预前的分布中去除因子<math>\Pr(G\mid S,R)</math>得到，其中do算子强行使 G 的值为真。下雨的可能性不受此干预的影响:
: <math>\Pr(R\mid\text{do}(G=T)) = \Pr(R).</math>
: <math>\Pr(R\mid\text{do}(G=T)) = \Pr(R).</math>