The pair-copula Bayesian Networks (PCBN) are graphical models composed of a directed acyclic graph (DAG) that represents (conditional) independence in a joint distribution. The nodes of the DAG are associated with marginal densities, and arcs are assigned with bivariate (conditional) copulas following a prescribed collection of parental orders. The choice of marginal densities and copulas is unconstrained. However, the simulation and inference of a PCBN model may necessitate possibly high-dimensional integration. We present the full characterization of DAGs that do not require any integration for density evaluation or simulations. Furthermore, we propose an algorithm that can find all possible parental orders that do not lead to (expensive) integration. Finally, we show the asymptotic normality of estimators of PCBN models using stepwise estimating equations. Such estimators can be computed effectively if the PCBN does not require integration. A simulation study shows the good finite-sample properties of our estimators.

翻译：配对Copula贝叶斯网络（PCBN）是由有向无环图（DAG）构成的图模型，用于表示联合分布中的（条件）独立性。DAG的节点与边缘密度函数相关联，边则根据指定的父节点顺序集合被赋予二元（条件）Copula函数。边缘密度函数和Copula函数的选择不受限制。然而，PCBN模型的模拟与推断可能需要可能高维的积分运算。本文完整刻画了在密度评估或模拟中无需任何积分运算的DAG结构特征。此外，我们提出一种算法，能够找出所有不会导致（高成本）积分运算的父节点顺序。最后，我们利用逐步估计方程证明了PCBN模型估计量的渐近正态性。若PCBN无需积分运算，此类估计量可被高效计算。模拟研究验证了所提估计量在有限样本下的优良性质。