Statistical Rethinking

3 Sampling the Imaginary

Lots of books on Bayesian statistics introduce posterior inference by using a medical testing scenario. To repeat the structure of common examples, suppose there is a blood test that correctly detects vampirism 95% of the time. This implies Pr(positive|vampire) = 0.95. It's a very accurate test. It does make mistakes, though, in the form of false positives. One percent of the time, it incorrectly diagnoses normal people as vampires, implying Pr(positive|mortal) = 0.01. The final bit of information we are told is that vampires are rather rare, being only 0.1% of the population, implying Pr(vampire) = 0.001. Suppose now that someone tests positive for vampirism. What's the probability that he or she is a bloodsucking immortal? ...