  In fully Bayesian analyses, prior distributions are specified before
observing data. Prior elicitation methods transfigure prior information into
quantifiable prior distributions. Recently, methods that leverage copulas have
been proposed to accommodate more flexible dependence structures when eliciting
multivariate priors. We prove that under broad conditions, the posterior cannot
retain many of these flexible prior dependence structures in large-sample
settings. We emphasize the impact of this result by overviewing several
objectives for prior specification to help practitioners select prior
dependence structures that align with their objectives for posterior analysis.
Because correctly specifying the dependence structure a priori can be
difficult, we consider how the choice of prior copula impacts the posterior
distribution in terms of asymptotic convergence of the posterior mode. Our
resulting recommendations streamline the prior elicitation process.
