A Bayesian Take on Colorectal Screening, Baseball, Fund Managers, and a Murder
This chapter is a slight departure from the previous chapters, being a commentary on how Bayes’ Theorem from the study of probability can illuminate a wealth of problems in the social and biological sciences.
It concerns conditional statements of the form “What is the probability of an event A given that some other event, B, has taken place?” I write this in shorthand as prob(A|B). The theorem in question relates this assertion to its mirror image prob(B|A), in which A and B are interchanged. I want to illustrate this idea by a number of unusual and perhaps-unfamiliar examples, although I begin with two better-known illustrations in order to ...