We consider predictive checking for Bayesian model assessment using leave-one-out probability integral transform (LOO-PIT). LOO-PIT values are conditional cumulative predictive probabilities given LOO predictive distributions and corresponding left out observations. For a well-calibrated model, LOO-PIT values should be near uniformly distributed, but in the finite sample case they are not independent, due to LOO predictive distributions being determined by nearly the same data (all but one observation). We prove that this dependency is non-negligible in the finite case and depends on model complexity. We propose three testing procedures that can be used for continuous and discrete dependent uniform values. We also propose an automated graphical method for visualizing local departures from the null. Extensive numerical experiments on simulated and real datasets demonstrate that the proposed tests achieve competitive performance overall and have much higher power than standard uniformity tests based on the independence assumption that inevitably lead to lower than expected rejection rate.

翻译：本文探讨利用留一法概率积分变换（LOO-PIT）进行贝叶斯模型评估的预测检验方法。LOO-PIT值是在给定留一法预测分布及相应剔除观测值的条件下计算的条件累积预测概率。对于校准良好的模型，LOO-PIT值应近似服从均匀分布，但在有限样本情形下，由于留一法预测分布由几乎相同的数据（仅剔除一个观测值）确定，这些值并不独立。我们证明在有限样本情形下这种依赖关系不可忽略，且其强度取决于模型复杂度。本文提出三种适用于连续与离散相关均匀值的检验程序，同时提出一种自动化图示方法用于可视化局部偏离零假设的情况。通过模拟数据与真实数据集的广泛数值实验表明，所提检验方法整体具有竞争优势，其检验功效显著高于基于独立性假设的标准均匀性检验——后者不可避免地导致低于预期的拒绝率。