Teaching Bayes’ Theorem: Strength of Evidence as Predictive Accuracy

Although teaching Bayes’ theorem is popular, the standard approach—targeting posterior distributions of parameters—may be improved. We advocate teaching Bayes’ theorem in a ratio form where the posterior beliefs relative to the prior beliefs equals the conditional probability of data relative to the marginal probability of data. This form leads to an interpretation that the strength of evidence is relative predictive accuracy. With this approach, students are encouraged to view Bayes’ theorem as an updating mechanism, to obtain a deeper appreciation of the role of the prior and of marginal data, and to view estimation and model comparison from a unified perspective.