We use the law of total variance to generate multiple expansions for the posterior predictive variance. These expansions are sums of terms involving conditional expectations and conditional variances and provide a quantification of the sources of predictive uncertainty. Since the posterior predictive variance is fixed given the model, it represents a constant quantity that is conserved over these expansions. The terms in the expansions can be assessed in absolute or relative sense to understand the main contributors to the length of prediction intervals. We quantify the term-wise uncertainty across expansions varying in the number of terms and the order of conditionates. In particular, given that a specific term in one expansion is small or zero, we identify the other terms in other expansions that must also be small or zero. We illustrate this approach to predictive model assessment in several well-known models.

翻译：我们利用总方差定律生成后验预测方差的多种展开式。这些展开式由包含条件期望和条件方差的项组成，能够量化预测不确定性的来源。由于后验预测方差在给定模型后是确定的，它在这些展开式中表现为守恒的常量。通过绝对或相对方式评估展开式中的各项，可理解预测区间长度的主要贡献因素。我们量化了不同项数和条件阶数下的展开式项级不确定性，特别地，当某个展开式中特定项很小或为零时，可识别其他展开式中必须同样很小或为零的对应项。本文通过若干经典模型展示了这一预测模型评估方法。