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That makes sense in the analytic case, but you mean in the monte-carlo case? I presume just 4D Newton's method on the final integral over the pdf_X to get the value we're looking for?

It makes sense, I'm just surprised the blog never comes out and says "you have to do a brute force search to get the parameters for the likelihoods A ~ Beta(2,13) and B ~ Beta(3,11) for P(B > A) to have about the right value".

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Your comment sounds very confused, can you elaborate? What do you mean “in the analytics case, but you mean in the monte carlo case?” I can’t parse that sentence as a response to the parent comment.

Further what do you mean by

> “ the blog never comes out and says "you have to do a brute force search to get the parameters for the likelihoods A ~ Beta(2,13) and B ~ Beta(3,11) for P(B > A) to have about the right value".”

What do you mean by “brute force search” here?

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