The Basic Bayesian Blunder
ROCHESTER UNIV NY DEPT OF PHILOSOPHY
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Direct Inference was distinguished from Inverse Inference early in the development of mathematical statistics. Direct Inference was the form of uncertain inference that took as premise a distribution in a population, and yielded a probable conclusion about the composition of a sample from the population. Inverse inference was to take as a premise the composition of a sample, and yield as a conclusion a probable conclusion about a distribution in a population. Direct inference seemed problematic. But inverse inference seemed to be needed to obtain the general premised needed for direct inference. Inverse inference proper is based on Bayesian principles. This paper argues that these principles are inconsistent with direct inference. It is concluded that we should hold fast to direct inference, and accept Bayesian procedures only when they can be put into the frame work of direct inference.
- Statistics and Probability