17.6 Beliefs, decisions and long-term error

Bayesianism is about beliefs, frequentism is about action choices (at least in the post-Fisherian, Neyman-Pearson and modern NHST variant). Bayesians can layer a decision procedure on top of the inferred probabilities, but they do not have to.

The Neyman-Pearson variant of frequentism, on the other hand, is inseparably tied to a choice criterion, thereby aiming to provide the long-term error control that motivates this approach. If Bayesian approaches adopt a fixed decision routine, like Kruschke’s ternary decision rules outlined in Chapter 11, they can be subjected to considerations of long-term error control. It can then even make sense to perform power calculations similar to those in the frequentist approach (usually: simulation based).