Approximate Bayesian Computation Applied to Nuclear Safeguards Metrology

Volume: 57, December 2018, pages 50-59

Authors: Tom Burr¹, Thomas Krieger², Claude Norman¹

¹_{Safeguards Information Management, International Atomic Energy Agency (IAEA),} ²_{Forschungszentrum Jülich}

Abstract: Approximate Bayesian Computation (ABC) is an inference option if a likelihood for measurement data is not available, but a forward model is available that outputs predicted observables, such as gamma counts, for any set of specified input parameters, such as item mass. This paper reviews ABC and illustrates how ABC can be applied in safeguards metrology. A key aspect of metrology is uncertainty quantification (UQ), approached from physical first principles (“bottom-up”) or approached empirically by comparing measurements from different methods and/or laboratories (“top-down”). Although ABC is not yet commonly used in metrology, an example using enrichment measurements is used to illustrate potential advantages in ABC compared to current bottom-up approaches. Using the same example, ABC is also shown to be useful in top-down UQ. And, the example shows good agreement between bottom-up and top-down measurement error relative standard deviation (RSD) estimates, while also allowing for the effects of itemspecific biases. As a diagnostic, in applications of ABC, the actual coverages of probability intervals are compared to the true coverages. For example, if an ABC-based interval for the true measurement RSD is constructed to contain approximately 95% of the true values, then one can check whether the actual coverage is close to 95%. It is shown that one advantage of ABC compared to other Bayesian approaches is its apparent robustness to miss-specifying the model while maintaining good agreement between the nominal and the actual coverage.

Keywords: approximate Bayesian computation; metrology; non-destructive assay; uncertainty quantification

Reference guideline:

Burr, T., Krieger, T., & Norman, C. (2018). Approximate Bayesian Computation Applied to Nuclear Safeguards Metrology. ESARDA Bulletin - The International Journal of Nuclear Safeguards and Non-proliferation, 57, 50-59. https://doi.org/10.3011/ ESARDA.IJNSNP.2018.10