In his book-length argument for likelihoodism, Royall (1997, 3) distinguishes the following three questions:
(1) What should you believe?
(2) What should you do?
(3) What does the present evidence say?
Likelihoodist methods are only intended to answer Question (3). In my view, the trouble with likelihoodism is that an answer to Question (3) is useful only insofar as it aids in answering Question (1) or (2), and likelihoodism does not provide an alternative to Bayesian and frequentist methods for answering Questions (1) and (2). Thus, while likelihoodism may be true, it is not a viable genuine alternative to Bayesian and frequentist methodologies.
I provide a more detailed argument for this view here. The next step in my project is to further develop this argument, primarily by considering possible likelihoodist responses. I currently have on my radar the following three responses:
(I) Characterizing one’s data as evidence is valuable in itself.
(II) The Law of Likelihood does in fact answer Royall’s questions (1) and (2), but only ceteris paribus.
(III) The Law of Likelihood provides a “frequentist methodology,” that is, a methodology that is justified by its operating characteristics.
My next series of posts will develop objections to these responses.
The wording I use for these questions is different from Royall’s and comes from (Sober 2008, 3).
Royall, R.M. 1997. Statistical Evidence: A Likelihood Paradigm. Monographs on Statistics and Applied Probability. London: Chapman & Hall.
Sober, Elliott. 2008. Evidence and Evolution: The Logic Behind the Science. Cambridge University Press.
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