Principles of Inference and Their Consequences

This paper argues that if inference is by way of Bayes’ theorem, then two data sets license different inferences or hypotheses if they register differences in the error probabilistic properties of the methods.

Abstract

What do data tell us about hypotheses or claims? When do data provide good evidence for or a good test of a hypothesis? These are key questions for a philosophical account of evidence and inference, and in answering them, philosophers of science have often appealed to formal accounts of probabilistic and statistical inference. In so doing, it is obvious that the answer will depend on the principles of inference embodied in one or another statistical account. If inference is by way of Bayes' theorem, then two data sets license different inferences only by registering differently in the Bayesian algorithm. If inference is by way of error statistical methods (e.g., Neyman and Pearson methods), as are commonly used in applications of statistics in science, then two data sets license different inferences or hypotheses if they register differences in the error probabilistic properties of the methods.