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 (Q${}^2$), 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.

翻译：在核设施退役项目中，放射性表征阶段旨在估算不同放射性核素的含量及空间分布。为进行估算，需在现场开展测量以获取初步信息。通常的工业实践是对这些数据应用空间插值工具（如普通克里金法），预测未观测位置处的污染目标值（如放射性核素浓度、放射性活度等）。本文针对普通克里金法因未考虑克里金参数（方差和变程）估算不确定性而导致的预测方差过度乐观这一已知问题提出质疑。为克服该问题，本文深入研究了贝叶斯克里金法的实际应用——该方法将模型参数视为随机变量。在小数据情境下（这在退役项目中常见），本文通过比较贝叶斯克里金法与普通克里金法的性能，论证了前者的有效性。该结论基于多个数值试验（采用不同模拟模型）及互补性验证准则获得，包括：预测性系数（Q${}^2$）、预测方差充分性（PVA）、$\alpha$置信区间图（及其相关均方误差alpha（MSEalpha））和预测区间充分性（PIA）。其中PIA是一种适应贝叶斯克里金法结果的新准则。最后，基于法国原子能委员会马尔库尔G3反应堆退役项目的真实数据集进行相同比较，验证了贝叶斯克里金法在工业放射性表征中的实际应用价值。