A statistical method for passive gamma ray tomography of nuclear waste vaults

This paper demonstrates a parameter identification problem encountered in the assay of intermediate-level nuclear waste vaults. A lumped parameter model of the vault contents is employed in which a likely geometry is assumed so as to reduce the number of unknown quantities in the resulting inverse problem. The inverse problem is tackled using Bayesian statistics, and the statistical distributions are sampled using a Markov chain Monte Carlo approach. The Bayesian approach affords flexibility in the specification of prior information: i.e. information that is known in advance of recording any measurements. Two parameterizations of the problem are considered: one involving five parameters and the other involving three parameters. It is shown that in order to obtain a satisfactory solution to the five-parameter problem a very specific type of prior information has to be specified, whereas for the three-parameter problem much less specific prior information is required. The inverse problem of identifying the model parameters in both the three-parameter and five-parameter formulations is solved with limited, but quantifiable precision.