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2 bayesian networks

  1. Jul 10, 2011 #1
    suppose i have 2 bayesian networks....
    a->b and c->d ie b depends on a and d depends on b
    now P(a,b,c,d)=P(a)*P(b|a)*P(c|a,b)*P(d|a,b,c)
    =P(a)*P(b|a)*P(c)*P(d|c)

    Am i right...?
    please reply..i need it as quickly as possible...
     
  2. jcsd
  3. Jul 10, 2011 #2
    It's not clear what you are trying to say since the term on the left is not a conditional probability.

    Note: [tex]P(A|B,C,D)= \frac{A\cap (B\cup C\cup D)}{B\cup C\cup D}[/tex]
     
    Last edited: Jul 10, 2011
  4. Jul 10, 2011 #3
    By ',' i mean intersection
    P(x,y)=p(x|y)*p(y)
    like this...
     
  5. Jul 10, 2011 #4
    OK, then the first line looks correct. However I don't know how the assumptions you're making regarding conditional independence allow you to get your simplification on the second line. If the two networks (a,b), (c,d) are conditionally independent, then I believe your simplifications are correct if they are taken individually. However, I'm not sure why you would combine them since they have no common variables.

    EDIT: In other words, am I supposed to know that P(c|a,b)=P(c)? How does the fact that d depends on c tell me that? (I assume that you made a mistake when you stated d depends on b since your formula indicates d depends on c.)
     
    Last edited: Jul 11, 2011
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