Bayesian Bottom-up Uncertainty Quantification in Neutron Multiplicity Measurements: Providing Uncertainty Distributions and Correlations in all the Assay-Item Parameters

摘要

Uncertainty quantification (UQ) for safeguards applications can be approached from physical first principles ("bottom-up") or approached empirically by comparing measurements from different methods and/or laboratories ("top-down"). The two approaches can lead to different estimates of uncertainty, often with the bottom-up uncertainty estimate being smaller than the top-down uncertainty estimate; such a gap between the estimates is the so-called "dark uncertainty" problem. One component of dark uncertainty is often item-specific biases that arise due to item-specific departures from calibration or modeling assumptions. In nondestructive assay of special nuclear material, inspectors bring instruments into the facility where standard modeling and/or calibration assumptions can be violated to varying degrees. More realistic models that allow for more physical effects can expose some of the dark uncertainty. In cases where the more realistic model does not lead to a tractable likelihood, approximate Bayesian computation (ABC) is an inference option. ABC can be used with the more realistic forward model, which outputs predicted observables (e.g. neutron counts) for any set of specified input parameters, such as item mass. This paper reviews ABC and illustrates how ABC can be applied in a neutron multiplicity counting case study in which some test items exhibit item-specific biases. As a diagnostic, when an ABC-based interval for the true measurement error relative standard deviation (RSD) is constructed to contain approximately 95% of the true values, one can check whether the actual coverage is close to 95%. The performance of ABC analysis is discussed in the framework of non-destructive assay in nuclear safeguards to illustrate potential advantages in ABC compared to current bottom-up approaches.