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Belief Networks (Conditional independence in Bayesian Networks)

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  • orondojones
    I ve read in the 2nd edition, that a node is conditionally independent of its non-descendants given its parents or given its Markov blanket. The 2nd edition
    Message 1 of 2 , May 3, 2007
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      I've read in the 2nd edition, that a node is conditionally independent
      of its non-descendants given its parents or given its Markov blanket.
      The 2nd edition makes reference to the 1st edition regarding d-
      separation and I have read the 1st edition's information about d-
      separation; however, I have come across in some additonal reading
      something called Berkson's paradox.

      This paradox seems to show circumstances that contradict the
      statements made about d-separation and Markov blankets. Am I correct
      in thinking that Berkson's paradox is an exception to rules regarding
      d-separation and Markov blankets?
    • Ivan F. Villanueva B.
      ... The so called Berkson s paradox states: if 0
      Message 2 of 2 , May 4, 2007
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        On Thu, May 03, 2007 07:37:59PM -0000, orondojones wrote:
        > I've read in the 2nd edition, that a node is conditionally independent
        > of its non-descendants given its parents or given its Markov blanket.
        > The 2nd edition makes reference to the 1st edition regarding d-
        > separation and I have read the 1st edition's information about d-
        > separation; however, I have come across in some additonal reading
        > something called Berkson's paradox.
        >
        > This paradox seems to show circumstances that contradict the
        > statements made about d-separation and Markov blankets. Am I correct
        > in thinking that Berkson's paradox is an exception to rules regarding
        > d-separation and Markov blankets?

        The so called Berkson's paradox states:

        if 0 < P(A) < 1 and 0 < P(B) < 1,
        and P(A|B) = P(A), i.e. they are independent,
        then P(A|B,C) < P(A|C) where C = A∪B (i.e. A or B).

        Where is the contradiction?

        --
        Iván F. Villanueva B.
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