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| ==举例== | | ==举例== |
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− | [[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 ]] |
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| The joint probability function is: | | The joint probability function is: |
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− | 对应的'''<font color="#ff8000"> 联合概率函数Joint probability function</font>'''是:
| + | 对应的联合概率函数是: |
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| 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)". |
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− | 其中G表示“草地湿了”,S表示“洒水器打开”,R表示下雨。
| + | 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)”。 |
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| 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 |
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− | 现在回答一个干预性的问题,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>'''
| + | 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>''' |
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| : <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> |
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| 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: |
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− | 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: |
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| : <math>\Pr(R\mid\text{do}(G=T)) = \Pr(R).</math> | | : <math>\Pr(R\mid\text{do}(G=T)) = \Pr(R).</math> |