Hey PeterPan2009.
Just to get things starting, can you show us what you've tried?
Hi,
I'm new when it comes to Bayesion networks and would be glad if someone could give me some hints on a problem.
I have the following probability distributions:
P(A)
P(B)
P(X|C)
P(Y|C)
P(C|A,B)
I would like to find P(A|X=true, Y= false). The domain of all variables are: true, false.
I have no idea how to start on this? Any tips?
Hi chiro!
Well, to be honest, I'm not sure how to start. That is, I'm not sure about the strategy to use to simplify the problem - in terms of the probabilities and distributions I know. The first step may be to use Bayes' rule like this (I'm not sure this is valid though):
And then marginalise over some variable?
This is what I have so far (I don't know if this is correct):
Using Bayes' rule:
Using marginalisation on C:
Using P(X,Y|C,A)P(C|A)=P(X,Y|C)P(C|A):
Using marginalisation on B:
Now I don't know what to do?
Updated:
Using Bayes' rule:
Using marginalisation on C:
Using P(X,Y|C,A)P(C|A)=P(X,Y|C)P(C|A):
Using marginalisation on B:
Hm, how do I sum out any variables. I have the distribution for P(C=c|B=b, A), but I dont have e.g. P(X=true, Y=false|C=c) only P(X=true|C=c) and P(y=false|C=c)?