Bayes' Theorem and the "Evidence-Based" Approach to Risk and Decision Analysis. S. Kaplan, Bayesian Systems Inc., 6000 Executive Boulevard, Suite 600, Rockville, MD 20852
What we call the "evidence-based" approach, to risk and decision, is both a philosophy and a methodology. The philosophy is that in public, private, and, especially, regulatory decision making, we should strive to "Let the Evidence Speak," as opposed to the personalities, opinions, positions, politics, special interests, or wishful thinkings. The methodology, which allows implementation of this philosophy, is Bayes’ Theorem, and is the fundamental mathematical principle governing the process of making logical inference from evidence.
The status of Bayes’ Theorem in the risk analysis community today is that after two centuries of being a "bad word," regarded in some quarters as a kind of mental disease, "Bayesian" has become a "good word." Two problems remain, however. One is that the theorem rests upon, as its foundation, the meaning of "probability," which itself has been the center of centuries worth of linguistic chaos, confusion and controversy. The second is that, for all but the simplest, "Grade A" types of evidence (i.e., pure, random double blind, sampling data), the theorem is not easy to apply, but requires creative, ad hoc techniques in each case. The current status of the theorem is thus like the first floor of a skyscraper, lacking a firm foundation, and needing upper stories showing how to handle evidence of other than this "Grade A" character.
The present paper will present a point of view, and definition of probability that we feel should clarify and settle the foundation issue once and for all. It will then present a series of examples showing how the theorem may be applied to evidence at various levels of indirectness, partial relevancy, and partial trustworthiness.