The Basic Bayesian Blunder

Bayesian statistical inference appears to offer a way to solve the problems of inferring general statistical distributions in populations from observed distributions in samples. Early in the development of mathematical statistics this form of inference was referred to as “inverse” inference, in contrast with “direct” inference, the inference from knowledge of a distribution in a population to a distribution in a sample. It was felt that direct inference was reasonably well understood, and that inverse inference was a problem. This paper argues that Bayesian techniques are based on principles that actually conflict with direct inference. It is concluded that we should hold fast to direct inference based on our knowledge of frequencies or chances, and accept Bayesian procedures only when they can be put into the framework of direct inference.