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.