We study the calibration of Gaussian process (GP) predictive distributions in the interpolation setting from a design-marginal perspective. Conditioning on the data and averaging over a design measure μ, we formalize μ-coverage for central intervals and μ-probabilistic calibration through randomized probability integral transforms. We introduce two methods. cps-gp adapts conformal predictive systems to GP interpolation using standardized leave-one-out residuals, yielding stepwise predictive distributions with finite-sample marginal calibration. bcr-gp retains the GP posterior mean and replaces the Gaussian residual by a generalized normal model fitted to cross-validated standardized residuals. A Bayesian selection rule-based either on a posterior upper quantile of the variance for conservative prediction or on a cross-posterior Kolmogorov-Smirnov criterion for probabilistic calibration-controls dispersion and tail behavior while producing smooth predictive distributions suitable for sequential design. Numerical experiments on benchmark functions compare cps-gp, bcr-gp, Jackknife+ for GPs, and the full conformal Gaussian process, using calibration metrics (coverage, Kolmogorov-Smirnov, integral absolute error) and accuracy or sharpness through the scaled continuous ranked probability score.

翻译：我们从设计边际的视角，研究插值设置下高斯过程（GP）预测分布的校准问题。通过以数据为条件并对设计测度μ取平均，我们利用随机化概率积分变换形式化定义了中心区间的μ覆盖度与μ概率校准。我们提出了两种方法：cps-gp通过标准化留一残差将保形预测系统适配于GP插值，产生具有有限样本边际校准的分段预测分布；bcr-gp保留GP后验均值，并将高斯残差替换为基于交叉验证标准化残差拟合的广义正态模型。一种基于后验方差上分位数（用于保守预测）或交叉后验Kolmogorov-Smirnov准则（用于概率校准控制）的贝叶斯选择规则，可在产生适用于序贯设计的平滑预测分布的同时，控制离散度与尾部行为。在基准函数上的数值实验比较了cps-gp、bcr-gp、GP的Jackknife+方法以及完全保形高斯过程，所用评估指标包括校准度量（覆盖度、Kolmogorov-Smirnov统计量、积分绝对误差）以及通过缩放连续排序概率得分衡量的准确度或锐度。