Auxiliary Assumptions and Epistemic Ratios: Fun with Bayes

Abstract

Although there have been many Bayesian analyses of the null hypothesis significance testing procedure, Bayesian thinking has not yet made strong inroads into theory testing (as opposed to hypothesis testing). We explain why this may be and how to introduce Bayesian thinking into theory testing. Bayesian evidence often comes in the form of empirical support for a hypothesis that was derived from a larger theory. We show that the probability of finding an empirical hypothesis to be true when a theory is true, and the probability of finding an empirical hypothesis to be true when a theory is false, are both fundamental in rigorous scientific knowledge accumulation. In turn, however, these conditional probabilities depend on the quality of the auxiliary assumptions that researchers use to traverse the distance from a more general theory to an empirical hypothesis. Therefore, we provide Bayesian analyses of theory testing that feature auxiliary assumptions. Our analyses implicate the importance of creativity o...