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.
Fields of Study & Subjects
Probabilistic and Robust Engineering Design
Soil Geostatistics and Mapping
Advanced Statistical Methods and Models
Publication details
- Journal / source
- ESAIM Probability and Statistics
- Publisher
- EDP Sciences
- Volume
- 30
- Pages
- 474–499
- Publication date
- 1 January 2026
- Language
- EN