Who's afraid Of Thomas Bayes?

Abstract

Sometimes direct evidence is so strong that a prescription for practice is decreed. Usually, things are not that simple—leaving aside the possibility that important trade offs may be involved, direct comparative data may be imprecise (especially in crucial sub-groups) or subject to possible bias, or there may be no direct comparative evidence; but still decisions have to be made. In these circumstances, indirect evidence—the plausibility of effects—enters the frame. But how should we describe the extent of plausibility and, having done so, how can this be integrated with any direct evidence that might exist. Also, how can allowance be made in a transparent (that is, explicit) way for perceptions of the size of bias in the direct evidence. Enter the Reverend Thomas Bayes; plausibility (however derived—laboratory experiment, qualitative study or just “experience”) is captured numerically as degrees of belief (“prior” to the direct data) and updated (by the direct evidence) to yield “posterior” probabilities for use in decision making. The mathematical model used for this purpose must explicitly take account of assumptions about bias in the direct data. This paradigm bridges theory and practice, and provides the intellectual scaffold for those who recognise that (numerically definable) probabilities, and values (also numerically definable) underlie decisions, but who also realise that subjectivity is ineluctable in science.