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We offer our two cents to the ongoing discussion on whether profilelikelihoods are "true" likelihood functions, by showing that the profilelikelihood function can in fact be identical to a marginal likelihood in thespecial case of normal models. Thus, profile likelihoods can be "true"likelihoods insofar as marginal likelihoods are "true" likelihoods. The priordistribution that achieves this equivalence turns out to be the Jeffreys prior.We suspect, however, that normal models are the only class of models for whichsuch an equivalence between maximization and marginalization is exact.

Are profile likelihoods likelihoods? No, but sometimes they can be