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arXiv · 2510.21277

Kriging measure-valued data with sparse observations: application to nuclear safety studies

Florian Gossard·François Bachoc·Jean Baccou·Thibaut Le Gouic·Jacques Liandrat·Tony Glantz
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Abstract

This work addresses the interpolation of probability measures within a spatial statistics framework. We develop a Kriging approach in the Wasserstein space, leveraging the quantile function representation of the one-dimensional Wasserstein distance. To mitigate the inaccuracies in semivariogram estimation that arise from sparse datasets, we combine this formulation with cross-validation techniques. In particular, we introduce a variant of the virtual cross-validation formulas tailored to quantile functions. The effectiveness of the proposed method is demonstrated on a controlled toy problem as well as on a real-world application from nuclear safety.

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Florian Gossard, François Bachoc, Jean Baccou, Thibaut Le Gouic, Jacques Liandrat, Tony Glantz. 2025-10-24. Kriging measure-valued data with sparse observations: application to nuclear safety studies. https://arxiv.org/abs/2510.21277

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