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. [Read more…]