Controversy over Bayes’ Theorem in the 21st Century
An article published in the June 7, 2013 article of Science Magazine entitled Bayes’ Theorem in the 21st Century by Bradley Efron (http://www.ime.usp.br/~abe/lista/pdfxeAKkfZxJM.pdf) looks at the controversy surrounding Bayes’ Theorem over the time at which Bayes published his paper (1763) all the way up until now. At first it seems odd that there would be so much controversy over a theorem, but the article explores several recent cases where Bayes’ Theorem was used and the outcome of the situation because of the implementation of the Theorem. I will discuss some of those in a minute, but first let me go back to the idea behind Bayes’ Theorem, which is a mathematical algorithm to determine probability based not only on current evidence but on prior experience as well. As we learned in class, P(A|B)=P(B|A)*P(A)/P(B); that is the probability of A given B is equal to the probability of B given A times the probability of A divided by the probability of B. One example the author gives where Bayes’ Theorem is necessary as compared to just present time statistical evidence is the case where a scientific study took significantly longer than expected but published results on their drug saying that statistically, the drug was successful. With that evidence alone, the FDA could approve the drug. BUT, if we take into account Bayes’ Theorem and ask WHY the study took so long and were given a response that the four previous trials all proved the drug unsuccessful, the FDA would reconsider their approval and say that one success does not validate four failures and thus take the drug off of the market. Here, Bayes’ Theorem works best in combining both current evidence and prior exchange. On the other hand, the author looks at examples where Bayes’ Theorem doesn’t exactly work. In particular he notes how, as an editor for an applied statistical journal, less than 1/4 of articles applied or even considered Bayes’ Theorem on the grounds that past experience may not always be readily available or validated. In fact, this makes alot of sense when considering that past experience can also be riddled with different factors. For example if you got a C this semester but you got all A’s the past 5 semesters, Bayes’ would take this into account and say that next semester you will probably receive an A when the data now may actually be more important because of the changed situations (maybe you got a permanent concussion; you changed to a much harder major; you took on two part time jobs; etc.) that will make it so that you continue to receive C’s in the upcoming future.
Efron concludes that he can’t really conclude anything. The controversy over Bayes’ Theorem continues on into the 21st century. He advises us to take into account Bayesian analysis only when prior information is both genuine and still valid in the current case but to be wary in cases where this information is lacking or possibly irrelevant. Let the controversy continue!