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We present three methodological improvements of the "SCK CEN approach" forBayesian inference of the radionuclide inventory in radioactive waste drums,from radiological measurements. First we resort to the Dirichlet distributionfor the prior distribution of the isotopic vector. The Dirichlet distributionpossesses the attractive property that the elements of its vector samples sumup to 1. Second, we demonstrate that such Dirichlet priors can be incorporatedwithin an hierarchical modeling of the prior uncertainty in the isotopicvector, when prior information about isotopic composition is available. Ourused Bayesian hierarchical modeling framework makes use of this availableinformation but also acknowledges its uncertainty by letting to a controlledextent the information content of the indirect measurement data (i.e., gammaand neutron counts) shape the actual prior distribution of the isotopic vector.Third, we propose to regularize the Bayesian inversion by using Gaussianprocess (GP) prior modeling when inferring 1D spatially-distributed quantities.As of uncertainty in the efficiencies, we keep using the same stylized drummodeling approach as proposed in our previous work to account for the sourcedistribution uncertainty across the vertical direction of the drum. A series ofsynthetic tests followed by application to a real waste drum show thatcombining hierarchical modeling of the prior isotopic composition uncertaintytogether with GP prior modeling of the vertical Pu profile across the drumworks well. We also find that our GP prior can handles both cases with andwithout spatial correlation. The computational times involved by our proposedapproach are on the order of a few hours, say about 2, to provide uncertaintyestimates for all variables of interest in the considered inverse problem. Thiswarrants further investigations to speed up the inference.

Improving Bayesian radiological profiling of waste drums using Dirichlet priors, Gaussian process priors, and hierarchical modeling