Monte Carlo test ($p_B=[1+{\sum }_{b=1}^B{1}_{\{T_b\ge T_{\mathrm{obs}}\}}]/(B+1)$)

Generate independent replicated datasets under a fully specified null hypothesis and calculate the same predictive discrepancy statistic for them and the observation. Their null exchangeability gives a finite-simulation rank test. The displayed add-one tail probability is valid with conservative treatment of ties, and avoids reporting zero solely because no replicate exceeds the observation.