Mark L. Taper
Montana State University-Bozeman
The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability.
Keywords Subjective probability  Objective probability  Propensity  Evidence  Confirmation  Prediction  Combining different types of probabilities  Bayesian decision theory   Evidential decision theory
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