Clinical decision-making demands uncertainty quantification that provides both distribution-free coverage guarantees and risk-adaptive precision, requirements that existing methods fail to jointly satisfy. We present a hybrid Bayesian-conformal framework that addresses this fundamental limitation in healthcare predictions. Our approach integrates Bayesian hierarchical random forests with group-aware conformal calibration, using posterior uncertainties to weight conformity scores while maintaining rigorous coverage validity. Evaluated on 61,538 admissions across 3,793 U.S. hospitals and 4 regions, our method achieves target coverage (94.3% vs 95% target) with adaptive precision: 21% narrower intervals for low-uncertainty cases while appropriately widening for high-risk predictions. Critically, we demonstrate that well-calibrated Bayesian uncertainties alone severely under-cover (14.1%), highlighting the necessity of our hybrid approach. This framework enables risk-stratified clinical protocols, efficient resource planning for high-confidence predictions, and conservative allocation with enhanced oversight for uncertain cases, providing uncertainty-aware decision support across diverse healthcare settings.

翻译：临床决策需要同时满足无分布覆盖保证与风险自适应精度的不确定性量化要求，而现有方法均无法兼顾这两点。本文提出一种贝叶斯-共形混合框架，以解决医疗预测领域的这一根本局限。该方法将贝叶斯层次随机森林与群体感知的共形校准相结合，利用后验不确定性对共形评分进行加权，同时保持严格的覆盖有效性。通过对美国3,793家医院、4个地区共61,538例住院病例的评估，本方法在实现目标覆盖率（实际94.3% vs 目标95%）的同时具备自适应精度：低不确定性病例的预测区间宽度缩减21%，而对高风险预测则相应拓宽。关键发现表明，仅依靠校准良好的贝叶斯不确定性会导致严重覆盖不足（14.1%），这凸显了本混合方法的必要性。该框架支持风险分层临床方案制定：对高置信度预测可实现高效资源规划，对不确定病例则通过强化监督实施保守资源配置，从而为多样化医疗场景提供具备不确定性感知的决策支持。