As a student in physics, I have experienced the “Why I am a Bayesian” lecture perhaps half a dozen times. It is always the same — the presenter smugly explains how the Bayesian interpretation is superior to the frequentist interpretation allegedly employed by the masses. They mention Bayes rule, marginalization, priors and posteriors.
What is the real story?
Is there a legitimate domain of applicability for frequentist statistics? (Surely in sampling or rolling a die many times it must apply?)
Are there useful probabilistic philosophies beyond “bayesian” and “frequentist”?
The Bayesian interpretation of probability suffices for practical purposes. But even given a Bayesian interpretation of probability, there is more to statistics than probability, because the foundation of statistics is decision theory and decision theory requires not only a class of probability models but also the specification of a optimality criteria for a decision rule. Under Bayes criteria, the optimal decision rules can be obtained through Bayes’ rule; but many frequentist methods are justified under minimax and other decision criteria.