{"ID":2850552,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.21277","arxiv_id":"2510.21277","title":"Kriging measure-valued data with sparse observations: application to nuclear safety studies","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.","short_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 fr...","url_abs":"https://arxiv.org/abs/2510.21277","url_pdf":"https://arxiv.org/pdf/2510.21277v1","authors":"[\"Florian Gossard\",\"François Bachoc\",\"Jean Baccou\",\"Thibaut Le Gouic\",\"Jacques Liandrat\",\"Tony Glantz\"]","published":"2025-10-24T09:23:59Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}