Rod Little

A seminal controversy in statistical inference is whether error probabilities associated with an inference method are evidentially relevant once the data are in hand. Frequentist error statisticians say yes; Bayesians say no. A “no” answer goes hand in hand with holding the Likelihood Principle (LP), which follows from inference by Bayes theorem. A “yes” answer violates the LP (also called the strong LP). The reason error probabilities drop out according to the LP is that it follows from the LP that all the evidence from the data is contained in the likelihood ratios (at least for inference within a statistical model). For the error statistician, likelihood ratios are merely measures of comparative fit, and omit crucial information about their reliability. A dramatic illustration of this disagreement involves optional stopping, and it’s the one to which Roderick Little turns in the chapter “Do you like the likelihood principle?” in his new book that I cite in my last post Continue reading →