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Topic: Conditional probability problem in the context of a simulation
Replies: 10   Last Post: Jan 27, 2011 5:01 AM

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Mike Lacy

Posts: 3
Registered: 1/20/11
Conditional probability problem in the context of a simulation
Posted: Jan 20, 2011 9:34 AM
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I'm trying to implement a simulation for a hypothesis testing problem
in which there is more than one way that the null hypothesis might be
true. The null hypothesis would be true if, say, either B = 0 or C =
0. Using "A" to represent the particular empirical evidence against
the null that is of interest, the p-value of interest would be
something like:

Prob[A | (B=0 or C=0)]

I can easily enough set up a simulation that constrains B = 0 and
simulate Prob(A|B=0), or similarly Prob(A|C=0), but I can't see anyway
to represent the constraint (B=0 or C = 0).

So, I'm wondering, as purely a matter of conditional probability, if
there is anyway to say anything about the value of
Prob[A | (B=0 or C=0)] in terms of Prob(A|B=0) and Prob(A|C=0)?

I tried proceeding from Prob[A and (B or C)] / Prob(B or C), but
didn't get anywhere.

I certainly can't see anything possible here, and I'd appreciate a
confirmation of this or (better yet, of course :-}) some kind of
solution.

Regards,
Mike Lacy



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