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Houshalter comments on Open thread, Sep. 26 - Oct. 02, 2016 - Less Wrong Discussion
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"Base rate" is statistics jargon. I would ask something like "which disease is more common?" And then if they still don't understand, you can explain that its probably the disease that is most common, without explaining Bayes rule.
Mightn't the vet have already factored the base rate in? Suppose x is the more common disease, but y is more strongly indicated by the diagnostics. In such a case it seems like the vet could be justified in saying that she cannot tell which diagnosis is accurate. For you to then infer that the dog most likely has x just because x is the more common disease would be putting undue weight on the Bayesian priors.