Evaluating Uncertain Evidence With Sir Thomas Bayes: A Note For Teachers

Abstract

Consider the following problem: On the night of March 1, 1986, in Lorain, Ohio, John Doe was struck by a speeding taxi as he crossed the street. The taxi was driving the wrong way down a one-way street and did not stop. An eyewitness thought that the taxi was blue. Doe has sued the Blue Cab Company for his medical expenses in a tort claim. Lorain has only two taxi companies, Blue Cab and Green Cab. Green Cab is the dominant firm with 85 percent of the taxis registered in the town. According to uncontroverted evidence, the eyewitness was 80 percent reliable in identifying the color of taxis; that is, he was able to identify the correct color of taxis 80 percent of the time, under conditions approximating those of the night of the accident. The case is being heard by a judge. Suppose the legal standard is “preponderance of the evidence.” What would you decide? How much weight to place on imperfect evidence is a problem of statistical inference. The correct statistical methodology of combining such evidence is called Bayes Theorem, after Sir Thomas Bayes, who devised the method.