Design-marginal calibration of Gaussian process predictive distributions: Bayesian and conformal approaches

• URL: http://arxiv.org/abs/2512.05611v1
• Date: Fri, 05 Dec 2025 10:53:20 GMT
• Title: Design-marginal calibration of Gaussian process predictive distributions: Bayesian and conformal approaches
• Authors: Aurélien Pion, Emmanuel Vazquez,
• Abstract summary: We study the calibration of Gaussian process (GP) predictive distributions in the setting from a design-marginal perspective.<n>We formalize -coverage for central intervals and -probabilistic calibration through randomized probability integral transforms.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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