Frequentist, Bayes, or Other?

Both philosophically and in practice, statistics is dominated by frequentist and Bayesian thinking. Under those paradigms, our courses and textbooks talk about the accuracy with which true model parameters are estimated or the posterior probability that they lie in a given set. In nonparametric problems, they talk about convergence to the true function (density, regression, etc.) or the probability that the true function lies in a given set. But the usual paradigms' focus on learning the true model and parameters can distract the analyst from another important task: discovering whether there are many sets of models and parameters that describe the data reasonably well. When we discover many good models we can see in what ways they agree. Points of agreement give us more confidence in our inferences, but points of disagreement give us less. Further, the usual paradigms’ focus seduces us into judging and adopting procedures according to how well they learn the true values. An alternative is to judge models and parameter values, not procedures, and judge them by how well they describe data, not how close they come to the truth. The latter is especially appealing in problems without a true model.