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. The resulting priors have been framed as suitable candidates for Bayesian analysis. We prove that under broad conditions, the posterior cannot retain many of these flexible prior dependence structures as data are observed. However, these flexible copula-based priors are useful for design purposes. 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 convergence of the posterior mode. We also make recommendations regarding prior dependence specification for posterior analyses that streamline the prior elicitation process.

翻译：在完全的贝叶斯分析中，先验分布在观测数据之前指定。先验启发方法将先验信息转化为可量化的先验分布。近期，基于连接函数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。由此产生的先验分布被视为贝叶斯分析的适宜候选。我们证明，在广泛条件下，随着数据观测，后验无法保留这些灵活先验依赖结构中的许多特征。然而，这些基于连接函数的灵活先验对于设计目的而言是有用的。由于先验正确指定依赖结构可能困难，我们考虑先验连接函数的选择如何通过后验模式的收敛性影响后验分布。此外，我们针对为简化先验启发过程的后续分析，提出关于先验依赖指定的建议。