{"ID":2832515,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.05611","arxiv_id":"2512.05611","title":"Design-marginal calibration of Gaussian process predictive distributions: Bayesian and conformal approaches","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.","short_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 integra...","url_abs":"https://arxiv.org/abs/2512.05611","url_pdf":"https://arxiv.org/pdf/2512.05611v1","authors":"[\"Aurélien Pion\",\"Emmanuel Vazquez\"]","published":"2025-12-05T10:53:20Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"stat.ME\"]","methods":"[]","has_code":false}