Asymptotically well-calibrated Bayesian $p$-value using the Kolmogorov-Smirnov statistic

Yueming Shen, Surya Tokdar

The posterior predictive $p$-value (ppp) is widely used in Bayesian model evaluation. However, due to double use of the data, the ppp may not be a valid $p$-value even in large sam…