Since being communicated to the Royal Society in 1763 by Reverend Thomas Bayes,5 the eponymous Theorem has exerted a near-fatal attraction on those exposed to it.6 Much as a bell placed on the cat would magically resolve so many of the problems of the average house mouse, Bayes’ straightforward, easily grasped mathematical formula would appear to provide the long-awaited basis for a robotic judge that is free of human prejudice.

On the plus side, Bayes’ Theorem offers three main advantages:

1. Simplifies the combination of a variety of different kinds of evidence, lab tests, animal experiments, and clinical trials, and serves as an effective aid to decision making.
2. Permits evaluating evidence in favor of a null hypothesis. And with very large samples, a null hypothesis is not automatically rejected.
3. Provides dynamic flexibility during the conduct of an experiment; sample sizes can be modified, measuring devices altered, subject populations changed, and end points redefined.

Suppose we have in hand a set of evidence E = {E1, E2, … , En}, and thus have determined the conditional probability Pr{A | E} that some event A is true. A might be the event that O. J. Simpson killed his ex-wife, that the Captain of the Exxon Valdez behaved recklessly, or some other incident whose truth or falsehood we wish to establish. An additional piece of evidence En +1 now comes to light. Bayes’ Theorem tell us that

where ∼A, read not A, is the event that A did not occur. ...

Get Common Errors in Statistics (and How to Avoid Them), 4th Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.