My prospectus may be taking shape. Last spring I was planning to use proofs of the Likelihood Principle to argue against the use of frequentist methods. Over the summer, I discovered a problem in my argument. The proofs of the Likelihood Principle that I was considering are valid and proceed from intuitively compelling premises; the problem with using them as an argument against frequentist methods is that the Likelihood Principle as it is formulated in those proofs only says that two experimental outcomes have the same “evidential meaning” if they have the same likelihood function. This claim implies that frequentist methods should not be used only on the assumption that a method that violates evidential equivalence should not be used. That assumption is questionable given that respecting evidential equivalence if the Likelihood Principle is true is incompatible with securing the kinds of guarantees about long-run operating operating characteristics that frequentist methods provide. One could plausibly maintain that securing those guarantees is more important than respecting evidential equivalence.
My current plan for my dissertation is to have four main chapters, each of which addresses objections to one aspect of frequentism: frequentism as a theory of probability, as a theory of evidence, as a theory of inference, and as a theory of decision. (Proofs of the Likelihood Principle fall under the heading of “objections to frequentism as a theory of evidence.”)
I should note that I don’t consider myself a frequentist, or a Bayesian. I claim only that the fact that frequentist methods have good long-run performance characteristics provides some (defeasible!) reason to use them, and that as a result frequentist methods are sometimes appropriate for use in science. For instance, frequentist methods seem entirely appropriate in the search for the Higgs boson, in which Bayesian methods are inappropriate because we have no reasonable basis for assigning prior probabilities.
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