  We present three methodological improvements of the "SCK CEN approach" for
Bayesian inference of the radionuclide inventory in radioactive waste drums,
from radiological measurements. First we resort to the Dirichlet distribution
for the prior distribution of the isotopic vector. The Dirichlet distribution
possesses the attractive property that the elements of its vector samples sum
up to 1. Second, we demonstrate that such Dirichlet priors can be incorporated
within an hierarchical modeling of the prior uncertainty in the isotopic
vector, when prior information about isotopic composition is available. Our
used Bayesian hierarchical modeling framework makes use of this available
information but also acknowledges its uncertainty by letting to a controlled
extent the information content of the indirect measurement data (i.e., gamma
and neutron counts) shape the actual prior distribution of the isotopic vector.
Third, we propose to regularize the Bayesian inversion by using Gaussian
process (GP) prior modeling when inferring 1D spatially-distributed quantities.
As of uncertainty in the efficiencies, we keep using the same stylized drum
modeling approach as proposed in our previous work to account for the source
distribution uncertainty across the vertical direction of the drum. A series of
synthetic tests followed by application to a real waste drum show that
combining hierarchical modeling of the prior isotopic composition uncertainty
together with GP prior modeling of the vertical Pu profile across the drum
works well. We also find that our GP prior can handles both cases with and
without spatial correlation. The computational times involved by our proposed
approach are on the order of a few hours, say about 2, to provide uncertainty
estimates for all variables of interest in the considered inverse problem. This
warrants further investigations to speed up the inference.

Data Analysis, Statistics and Probability;Instrumentation and Detectors