A comparison between Bayesian and ordinary kriging based on validation criteria: application to radiological characterisation

Martin Wieskotten (1, 2) , Marielle Crozet (2, 3) , Bertrand Iooss (4, 5, 6) , Céline Lacaux (1) , Amandine Marrel (6, 7)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 ISEC - Institut des Sciences et technologies pour une Economie Circulaire des énergies bas carbone
3 CETAMA - Commission des méthodes d'analyse du CEA
4 EDF R&D PRISME - Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation
5 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
6 IMT - Institut de Mathématiques de Toulouse UMR5219
7 IRESNE - Institut de recherche sur les systèmes nucléaires pour la production d'énergie bas carbone (CEA - DES)

In decommissioning projects of nuclear facilities, the radiological characterisation step aims to estimate the quantity and spatial distribution of different radionuclides. To carry out the estimation, measurements are performed on site to obtain preliminary information. The usual industrial practice consists in applying spatial interpolation tools (as the ordinary kriging method) on these data to predict the value of interest for the contamination (radionuclide concentration, radioactivity, etc.) at unobserved positions. This paper questions the ordinary kriging tool on the well-known problem of the overoptimistic prediction variances due to not taking into account uncertainties on the estimation of the kriging parameters (variance and range). To overcome this issue, the practical use of the Bayesian kriging method, where the model parameters are considered as random variables, is deepened. The usefulness of Bayesian kriging, whilst comparing its performance to that of ordinary kriging, is demonstrated in the small data context (which is often the case in decommissioning projects). This result is obtained via several numerical tests on different toy models, and using complementary validation criteria: the predictivity coefficient (Q²), the Predictive Variance Adequacy (PVA), the $\alpha$-Confidence Interval plot (and its associated Mean Squared Error alpha (MSEalpha)), and the Predictive Interval Adequacy (PIA). The latter is a new criterion adapted to the Bayesian kriging results. Finally, the same comparison is performed on a real dataset coming from the decommissioning project of the CEA Marcoule G3 reactor. It illustrates the practical interest of Bayesian kriging in industrial radiological characterisation.

Mots clés: kriging; geostatistics; uncertainty; model validation

Domaines: Statistiques [math.ST]

Martin Wieskotten, Marielle Crozet, Bertrand Iooss, Céline Lacaux, Amandine Marrel. A comparison between Bayesian and ordinary kriging based on validation criteria: application to radiological characterisation. Mathematical Geosciences, 2023, pp.10.1007/s11004-023-10072-y. ⟨10.1007/s11004-023-10072-y⟩. ⟨hal-03806713v3⟩