Bayesian Statistics Applied to the Activities of Waste Drums

Gamma spectrometry is widely used to determine the radioactive content of waste drums. However, the results of such surveys often result in large numbers of limit-of-detection (LOD) results. In a previous paper it was shown how simple statistical methods could be used to make estimates of the mean activity of a set of waste drums even when the individual measurements were dominated by limit-of-detection results. In that approach it was necessary to make assumptions about the statistical distribution (taken to be lognormal) of the activities and the geometric standard deviations of the distributions. In this paper a development of the method is presented which uses two statistical methods — Bayes’ Theorem and marginalization. These allow the probability distribution of the mean activity of the waste drums to be calculated, whilst the number of assumptions is reduced to just one, namely the form of the statistical distribution. The mathematical details are described in the paper and the application to a set of U235-in-drum measurements is presented.