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：我们考虑使用留一概率积分变换（LOO-PIT）进行贝叶斯模型评估的预测检验。LOO-PIT 值是给定留一预测分布及相应留出观测值时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，由于留一预测分布由几乎相同的数据（仅少一个观测值）决定，这些值并不独立。我们证明这种依赖关系在有限样本中不可忽略，且依赖于模型复杂度。我们提出了三种可用于连续和离散相依均匀值的检验方法。我们还提出了一种自动图形化方法，用于可视化与零假设的局部偏离。在模拟和真实数据集上进行的大量数值实验表明，所提出的检验方法在整体上实现了有竞争力的性能，并且其功效远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。