Bayesian and Evidential Paradigms

The first step is to distinguish two questions: 1. Given the data, what should we believe, and to what degree? 2. What kind of evidence do the data provide for a hypothesis H 1 as against an alternative hypothesis H 2 , and how much? We call the first the “confirmation”, the second the “evidence” question. Many different answers to each have been given. In order to make the distinction between them as intuitive and precise as possible, we answer the first in a Bayesian way: a hypothesis is confirmed to the extent that the data raise the probability that it is true. We answer the second question in a Likelihoodist way, that is, data constitute evidence for a hypothesis as against any of its rivals to the extent that they are more likely on it than on them. These two simple ideas are very different, but both can be made precise, and each has a great deal of explanatory power. At the same time, they enforce corollary distinctions between “data” and “evidence”, and between different ways in which the concept of “probability” is to be interpreted. An Appendix explains how our likelihoodist account of evidence deals with composite hypotheses.