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

arXiv: https://arxiv.org/abs/2512.05611 · HTML: https://mlsanity.com/paper/2512.05611/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2025.

## Built on by (most cited first, 2 of 2)

- [Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2605.20145/) (2026)
- [Probabilistic Data-Driven Modelling of Astrophysical Transients: The Neural Process Family for Ultrafast and Class-Agnostic Light Curve Reconstruction with NightLANP](https://mlsanity.com/paper/2605.27527/) (2026)

## Abstract (arXiv)

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.