Bayesian posterior predictive densities as non-conformity scores and Bayesian quadrature are used to estimate and minimise the expected prediction set size. Operating within a split conformal framework, BCP provides valid coverage guarantees and demonstrates reliable empirical coverage under model misspecification. Across regression and classification tasks, including distribution-shifted settings such as ImageNet-A, BCP yields prediction sets of comparable size to split conformal prediction, while exhibiting substantially lower run-to-run variability in set size. In sparse regression with nominal coverage of 80 percent, BCP achieves 81 percent empirical coverage under a misspecified prior, whereas Bayesian credible intervals under-cover at 49 percent.

翻译：本文采用贝叶斯后验预测密度作为非共形性评分，并运用贝叶斯积分来估计和最小化预测集的期望规模。在分割共形框架下，BCP方法能够提供有效的覆盖保证，并在模型设定错误的情况下展现出可靠的实证覆盖性能。在回归与分类任务中（包括ImageNet-A等分布偏移场景），BCP产生的预测集规模与分割共形预测相当，但其运行间集合规模的变异度显著更低。在名义覆盖率为80%的稀疏回归任务中，即使先验分布设定错误，BCP仍能实现81%的实证覆盖率，而贝叶斯可信区间仅达到49%的覆盖率。