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In this case, the objective is to derive the joint probability P(A and B) from the conditional P(A|B). Consequently, the correct prior term of the Bayesian numerator is P(B) and NOT the conditional P(B|A) because P(A|B) X P(B|A) ≠ P(A and B). Rather, the correct P(B) to use as the prior for table two is the sum of the updated posterior conditional ...


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You didn’t need to use Bayes theorem to calculate P(B|A) for table 1 - you could’ve calculated it the same way you did P(A|B). Probably would use Table 1’s P(B|A) and not P(B). Should probably use table 1’s posterior as the prior for Table 2. Even though the formula looks like it should be P(B), but that makes no sense to actually literally use table 1’s P(...


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I wanted to post this as a comment but I do not have enough reputation. I found this write up to be helpful: http://ntur.lib.ntu.edu.tw/bitstream/246246/20060927122912664791/1/gpr.pdf


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The Cauchy prior was suggested by Jeffreys solely for testing. On the basis (Chapter V, Section 2) of giving all the mass to the alternative when the observation is not zero and the sample variance zero, as shown in my slides above (taken from a seminar series I gave on Jeffreys' book), where (in Jeffreys' notations) $K$ denotes the Bayes factor, $f(\cdot)$ ...


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