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. In more precise and mathematical notation, Pr(positive test result|vampire) = 0.95. It’s a very accurate test, nearly always catching real vampires. It also make mistakes, though, in the form of false positives. One percent of the time, it incorrectly diagnoses normal people as vampires, Pr(positive test result| 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 ...
