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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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Dan Heyman

Posts: 179
Registered: 12/13/04
Re: Conditional probability problem in the context of a simulation
Posted: Jan 20, 2011 5:42 PM
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On Jan 20, 9:34 am, Mike Lacy <> wrote:
> 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

If B and C are independent you don't have a problem, so I'll assume
they're dependent. Can you arrange for both B=0 and C=0? If so, use
P{B or C}=P{B}+P{C}-P{BC}.

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