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

TL;DR

This paper introduces a novel Kriging method for interpolating probability measures in spatial statistics using Wasserstein space, enhanced with cross-validation to handle sparse data, demonstrated on nuclear safety applications.

Contribution

It develops a Wasserstein space Kriging approach for measure-valued data and introduces a tailored cross-validation technique for sparse datasets.

Findings

Effective interpolation of probability measures demonstrated on toy and real-world nuclear safety data.

Improved accuracy in sparse data scenarios through combined Wasserstein Kriging and cross-validation.

Validated approach shows promise for nuclear safety and other applications involving measure-valued data.

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.