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