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

TL;DR

This paper enhances Bayesian methods for radioactive waste drum analysis by integrating Dirichlet priors, hierarchical modeling, and Gaussian process priors to improve isotopic and spatial profile inference, demonstrated through synthetic and real data.

Contribution

It introduces a novel combination of Dirichlet, hierarchical, and Gaussian process priors for improved Bayesian inference in waste characterization.

Findings

Hierarchical modeling improves isotopic composition estimates.

GP priors effectively model spatially-distributed quantities.

Method achieves accurate uncertainty quantification within a few hours.

Abstract

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.