Bayésienne Réseau: Indépendance et indépendance conditionnelle

Question

Je vais avoir un malentendu en ce qui concerne le réseau bayésien. Mon principal malentendu sont l'indépendance et l'indépendance conditionnelle !!

Si par exemple Je dois calculer P(Burglary|Johncall), est-ce P(Burglary|Johncalls)=P(Burglary) parce que je vois que Cambriolage est indépendante de Johncalls ??

Answer 1

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.