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I have the following Bayes network enter image description here

Is it possible to get probability of P(X|ABC) if I have only the probabilities P(X|A), P(X|B), P(X|C) ?

Thanks.

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No it is not. You are welcome. –  Did Sep 15 '12 at 14:25
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1 Answer 1

up vote 1 down vote accepted

Are A, B and C independent based on the network diagram? If so P(X|ABC)=P(XABC)/P(ABC)=

P(XABC)/[P(A) P(B) P(C)] = P(XBC|A)/[P(B) P(C)] =P(XAB|C)/[P(A) P(B)]=P(XAC|B)/[P(A) P(C)].

So you need to know two of these 3 probabilities P(A) P(B) and P(C) along with the appropriate one from P(XAB|C), P(XBC|A) and P(XAC|B).

You can't get these probabilities directly from knowing P(X}A) P(X|B) and P(X|C).

Did's comment/answer is correct.

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Thanks guys! ;) –  Anton Sep 16 '12 at 6:10
    
Anton: Sorry for the ruckus. (But I did answer your question... :-) and if more explanations are needed, you may simply ask for them.) –  Did Sep 16 '12 at 8:15
    
@Anton Although the question is asked in a form that yes or no would be an answer, you and I and probably even did know that would not be satisfactory. I think my answer gave a satisfactory explanation. An answer should not require much elaboration and a comment that just says "No it is not. You are welcome" is not at all helpful. Did acknowledges downvoting my answer even though it is correct. My insert about his smug comment is not appropriate for inclusion in an answer. that seems to be the basis of him downvote. I will remove it and let's see if it gets the downvote retracted. –  Michael Chernick Sep 16 '12 at 12:17
    
Post undownvoted, despite some dubious assertions in last comment. –  Did Sep 16 '12 at 12:22
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@did Okay, we haven't hit it off very well on this site. I do think a simple no answer in a remark to this question is not very helpful even though it is correct. I also do need to be precise with answers to questions as you have noted at times even though I think a particular downvote on one question that you gave was not apporiate. I do appreciate that you have the courage of your convictions to mention why you give downvotes when you do. You generally give very good contributions on this site as seen by your very high rep. Can we declare a truce? –  Michael Chernick Sep 16 '12 at 12:48
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