
Re: Conditional probability problem in the context of a simulation
Posted:
Jan 20, 2011 5:42 PM


On Jan 20, 9:34 am, Mike Lacy <mgl...@gmail.com> 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 pvalue 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(AB=0), or similarly Prob(AC=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(AB=0) and Prob(AC=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}.

