贝叶斯网络：独立性和条件独立性
我对贝叶斯网络有一些误解。我的主要误解是独立和有条件的独立！
如果例如我必须计算 P(入室行窃|Johncall), 是 P(Burglary|Johncalls)=P(Burglary) 因为我发现 Burglary 独立于 Johncalls 吗？
I'm having some misunderstanding concerning Bayesian network. My main misunderstanding are independence and conditional independence!!
If e.g. I have to calculateP(Burglary|Johncall),
is it P(Burglary|Johncalls)=P(Burglary) because i'm seeing that Burglary is independent of Johncalls??
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入室盗窃独立于 JohnCalls 给出警报。所以 P(B|A,J) = P(B|A)。
解释示例
这个想法是，约翰只能告诉您有警报。但如果您已经知道有警报，那么约翰打来的电话不会告诉您有关入室盗窃可能性的任何新信息。是的，您知道约翰听到了警报，但这不是您在询问入室盗窃时感兴趣的内容。
有条件独立
在学校里，您可能已经了解了无条件独立，当 P(A|B) = P(A)*P(B) 时给出。无条件独立使得计算变得容易，但很少发生——在信念网络内，无条件独立的节点将是不连接的。
另一方面，条件独立稍微复杂一些，但发生的频率更高。这意味着当了解到另一个“分离”事实时，两个事件的概率变得彼此独立。
Burglary is independent from JohnCalls given Alarm. So P(B|A,J) = P(B|A).
Explaining the example
The idea is, that John can only tell you that there is an alarm. But if you already know that there is an alarm, then the phone call from John will tell you nothing new about the possibility of a burglary. Yes, you know that John heard the alarm, but that's not what you're interested in when asking for Burglary.
Conditional Independence
In school, you've probably learned about unconditional independence, given when P(A|B) = P(A)*P(B). Unconditional independence makes things easy to calculate but happens pretty rarely - inside the belief network unconditionally independent nodes would be unconnected.
Conditional independence on the other hand is a bit more complicated but happens more often. It means that the probability of two events becomes independent of each other when another "separating" fact is learned.