Bayesian decision tree posterior for uncertainty-aware trauma mortality prediction: a benchmark on CRASH-2, CRASH-3, and ICU cohorts

{Methods:}We benchmark \RJBDT{} on four datasets: the CRASH-2 trauma RCT (n=20{,}184), the CRASH-3 TBI RCT (n=12{,}672), PhysioNet CinC~2012 (n=8{,}000), and a stratified Kaggle ICU cohort (n=20{,}000). Comparators are split conformal prediction, a bootstrap GBM quantile ensemble, and a bagging decision-tree ensemble. Evaluation spans eight metrics: AUROC, Brier score, ECE, PICP, MPIW, CRPS, NLPD, and decision curve analysis (DCA). Robustness under 0--40% MCAR missingness is also assessed.{Results:}On CRASH-2 and CRASH-3, \RJBDT{} achieves AUROC of 0.828 and 0.836, competitive with published logistic-regression baselines (0.822 and 0.843) and above the IMPACT~Core reference (0.816). It achieves the best calibration on CRASH-2 (ECE~= 0.005, 6.7\times lower than the next-best baseline), the closest-to-nominal prediction interval coverage among all non-trivial methods (mean gap 3.0~pp from the 0.95 target, MPIW~0.17--0.26), and positive net benefit across decision thresholds 5--30% on both trauma cohorts. Under 40% MCAR missingness, AUROC degrades by only 5.2~pp and PICP by 1.7~pp. \RJBDT{} is the only evaluated method providing CRPS and NLPD proper scoring.{Conclusions:}Among the four evaluated methods, \RJBDT{} is the only approach simultaneously achieving near-nominal coverage, best-in-class calibration, and a full predictive posterior enabling decision curve analysis and proper scoring rules. These properties make it directly applicable to uncertainty-aware triage protocols in trauma care.