Bayesian inference based on a bivariate gamma distribution of Kibble for low-level radioactivity detection in nuclear decommissioning operations

Abstract

Statistical test analysis has proven itself to be versatile tool in various scientific and technical fields, following either a frequentist approach based on a p−value, or a Bayesian approach evaluating a Bayes factor. In this study, the authors adapted a Bayesian approach to a radiation-detection application in the industrial context of nuclear decommissioning. The detection of a weak uranium signal on concrete, under the constraint of a very low signal-to-noise ratio, represents in particular a major challenge in this application area. For this purpose, we developed an original Bayesian statistical hypothesis test based on a bivariate gamma distribution of Kibble. Said test allows merging the absolute and relative characters of two Bayesian tests developed in the same context, as well as providing better performance tradeoff in both cases of stationary and non-stationary radiological backgrounds. The simulation-based study showed that the proposed Bayesian test should meet the abovementioned expectations, and allow the detection of a relatively low surface activity uranium contamination, while ensuring a competitive tradeoff between statistical sensitivity and specificity.