A Primer on Bayesian Approaches to Hypothesis-testing

The Bayesian approach to testing hypotheses has two critical elements. First, a Bayesian approach stands the classical (by which I mean frequentist but I can’t bring myself to type these “ist” designations) approach on its head. In the classical approach, our questions revolve around the probability of the data, given a specific hypothesis. In the Bayesian approach, our questions revolve around the probability of various hypotheses, given the data. You can see that the derivation of Bayesian methods will involve the same assumptions and manipulations of conditional probabilities that we discussed when we covered Bayesian estimation methods.