Jerzy Neyman sometimes motivated his theory of confidence intervals by appealing to what he called “the classical point of view in the theory of probability,” which he characterized as saying that the claim that a given event has probability p implies that the relative frequency of that event will be approximately equal to p in a long series of trials (e.g. Neyman 1941, 376-378). In general, most statistical frequentists favor an “objective” interpretation of probability in terms of either long-run frequencies or propensities. Thus, objections to frequency and propensity interpretations appear to be threats to statistical frequentism.
However, it is not at all clear to me that a statistical frequentist needs to be a probability objectivist. One can hold that a subjective interpretation is perfectly coherent and even the best explication of probability without thinking that Bayesian methods are always the best methods to use in science. Perhaps probabilities are best thought of as degrees of belief but science isn’t about having diachronically coherent degrees of belief.
Statistical frequentists do seem to need to be able to claim that the long-run operating characteristics of their methods have an objective status in order for their methods to have any appeal. However, they can make that claim if they can show simply that a frequency or propensity interpretation is viable as applied to the probabilities that figure in the operating characteristics of their methods. The question, then, is whether standard objections to various forms of probabilistic objectivism apply to these probabilities.
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