Comments on Confidence as Likelihood by Pawitan and Lee in Statistical Science, November 2021

Abstract

Pawitan and Lee (Statist. Sci. 36 (2021) 509–517) attempt to show a correspondence between confidence and likelihood, specifically, that “confidence is in fact an extended likelihood” (Statist. Sci. 36 (2021) 509–517, abstract). The word “extended” means that the likelihood function can accommodate unobserved random variables such as random effects and future values; see (J. Amer. Statist. Assoc. 91 (1996) 791–806) for details. Here, we argue that the extended likelihood presented by (Statist. Sci. 36 (2021) 509–517) is not the correct extended likelihood and does not justify interpreting confidence as likelihood.