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Re: [aima-talk] Belief Networks (Conditional independence in Bayesian Networks)

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  • Ivan F. Villanueva B.
    ... The so called Berkson s paradox states: if 0
    Message 1 of 2 , May 4, 2007
      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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