We use the law of total variance to generate multiple expressions for the posterior predictive variance in Bayesian hierarchical models. These expressions are sums of terms involving conditional expectations and conditional variances. Since the posterior predictive variance is fixed given the hierarchical model, it represents a constant quantity that is conserved over the various expressions for it. The terms in the expressions can be assessed in absolute or relative terms to understand the main contributors to the length of prediction intervals. Also, sometimes these terms can be intepreted in the context of the hierarchical model. We show several examples, closed form and computational, to illustrate the uses of this approach in model assessment.

翻译：我们运用全方差定律推导了贝叶斯分层模型中后验预测方差的多种表达式。这些表达式由涉及条件期望与条件方差的项求和构成。由于后验预测方差在给定分层模型时是确定的，它代表了一个在各类表达式中保持不变的守恒量。可通过绝对或相对方式评估表达式中的各项，以理解预测区间长度的主要贡献源。在某些情况下，这些项可在分层模型的背景下进行解释。我们通过闭式解与计算实例展示了该方法在模型评估中的应用。