2025/04/18 by Shen, Yueming
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2504.14077
The posterior predictive p-value is a widely used tool for Bayesian model checking. However, under most test statistics, its asymptotic null distribution is more concentrated around 1/2 than uniform. Consequently, its finite-sample behavior is difficult to interpret and tends to lack power, which is a well-known issue among practitioners. A common choice of test statistic is the Kolmogorov-Smirnov test with plug-in estimators. It provides a global measure of model-data discrepancy for real-valued observations and is sensitive to model misspecification. In this work, we establish that under this test statistic, the posterior predictive p-value converges in distribution to uniform under the null. We further use numerical experiments to demonstrate that this p-value is well-behaved in finite samples and can effectively detect a wide range of alternative models.