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.

翻译：在全贝叶斯分析中，先验分布是在观测数据之前指定的。先验启发方法将先验信息转化为可量化的先验分布。近年来，基于copula的方法被提出以在启发多元先验时容纳更灵活的依赖结构。我们证明，在广泛条件下，后验分布无法在大样本设定中保留这些灵活的依赖结构。通过概述先验指定的若干目标，我们强调这一结果的影响，以帮助实践者选择与其后验分析目标相一致的目标先验依赖结构。由于正确指定先验依赖结构可能较为困难，我们考察了先验copula选择如何通过后验模式的渐近收敛性影响后验分布。由此得出的建议简化了先验启发过程。