Bayesian Updating of Material Balances Covariance Matrices Using Training Data



Published Nov 1, 2020
T. Burr M.S. Hamada


The main quantitative measure of nuclear safeguards effectiveness is nuclear material accounting (NMA), which consists of sequences of measured material balances that should be close to zero if there is no loss of special nuclear material such as Pu. NMA is essentially “accounting with measurement errors,” which arise from good, but imperfect, measurements. The covariance matrix MB of a sequence of material balances is the key quantity that determines the probability to detect loss. There is a recent push to include process monitoring (PM) data along with material balances from NMA in new schemes to monitor for material loss. PM data includes near-real-time measurements by the operator to monitor and control process operations. One concern regarding PM data is the need to estimate normal behavior of PM residuals, which requires a training period prior to ongoing testing for material loss. Assuming that a training period is used for PM data prior to its use in statistical testing for loss, that same training period could also be used for improving the estimate of MB that is used in NMA. We consider updating MB using training data with a Bayesian approach. A simulation study assesses the improvement gained with larger amounts of training data.

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nuclear material accounting, process monitoring, Bayesian updating of covariance matrix

Aigner, H., et al. (2010). International Target Values 2010 for Measurement Uncertainties in Safeguarding Nuclear Materials, Journal of Nuclear Materials Management 30(2), available at
Avenhaus, R. and Jaech, J. (1981). On Subdividing Material Balances in Time and/or Space, Journal of Nuclear Material Management, 10, 24-33.
Beedgen, R. (1987). Present and Future Aspects of PROSA - a Computer Program for Near Real Time Accountancy, Proceedings of 28th Annual Meeting of the Institute of Nuclear Materials Management.
Burr, T., Hamada, M.S. (2014a). Smoothing and Time Series Modeling of Nuclear Material Accounting Data for Protracted Diversion Detection, to appear Nuclear Science and Engineering.
Burr, T., Hamada, M.S, Ticknor, L, Weaver, B. (2014b). Model Selection and Change Detection for a Time-varying Mean in Process Monitoring, Nuclear Instruments and Methods in Physics Research A 751, 79-87.
Burr, T., Hamada, M.S. (2014c). Bayesian Updating of the Material Balances Covariance Matrices with Training Data, Los Alamos National Laboratory report LA-UR-14-22154.
Burr, T. and Hamada, M.S. (2013a). Revisiting Statistical Aspects of Nuclear Material Accounting. Science and Technology of Nuclear Installations, Article ID 961360, 15 pages, DOI:10.1155/2013/961360.
Burr, T., Hamada, M.S., Howell, J., Skurikhin, M., Ticknor, L., Weaver, B. (2013b). Estimating Alarm Thresholds For Process Monitoring Data Under Different Assumptions About The Data Generating Mechanism, Science and Technology of Nuclear Installations, Volume 2013, Article ID 705878, 18 pages, DOI:10.1155/2013/705878.
Burr, T., Hamada, M.S., Skurikhin, M., Weaver, B. (2012). Pattern Recognition Options To Combine Process Monitoring And Material Accounting Data In Nuclear Safeguards, Statistics Research Letters 1(1), 6-31.
Burr, T., Coulter, C., Hakkila, E., Ai, H., Kadokura, I., Fujimaki, K. (1995). Statistical Methods for Detecting Loss of Materials Using Near-Real Time Accounting Data, Proceedings of the 36th Annual Meeting of the Institute of Nuclear Materials Management.
Casella, G. and George E.I. (1992). Explaining the Gibbs Sampler. The American Statistician, 46, 327-335.
Chib, S. and Greenberg, E. (1995). Understanding the Metropolis Hastings Algorithm. The American Statistician, 49, 327-335.
Downing, D.J., Pike, D.H., and Morrison, G.W. (1978). Analysis of MB data Using ARIMA models, Nuclear Materials Management, 7(4), 80-86.
Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (2003). Bayesian Data Analysis, Second Edition. Boca Raton: Chapman and Hall.
Goldman, A.S., Picard, R.R., and Shipley, J.P. (1992). Statistical Methods for Nuclear Materials Accounting: an Overview, Technometrics, 24(4), 267-281.
Grznar, J., Booth, D.E., and Sebastian, P. (1997). The Use of Robust Smoothers in Nuclear Material Safeguards, Journal of Chemical Information and Computer Sciences, 37, 236-240.
Hamburg, J.H., Booth, D.E., and Weinroth, G.J. (1996). A Neural Network Approach to the Detection of Nuclear Material Losses, Journal of Chemical Information and Computer Sciences, 36, 544-553.
Howell, J., Bevan, G., Burr, T. (2013). Inspector Interfaces to Facilitate Subjective Reasoning about Quantities in Trends, Computers and Chemical Engineering, 48, 29-39.
Jones, B. (1989). Near Real Time Materials Accountancy Using SITMUF and a Joint Pages Test: Improvement of the Test, ESARDA Bulletin, 16, 13-19.
Page, E. (1955). A Test for a Change in a Parameter Occurring at an Unknown Point, Biometrika 42, 523-527.
Prasad, S., Booth, D., Hu, M.Y., and Deligonul, S. (1995a). The Detection of Nuclear Materials Losses. Decision Sciences, 26, 265-281.
Prasad, S., Booth, D., and Hu, M.Y. (1995b). Monitoring the Quality of a Chemical Production Process Using the Joint Estimation Method, Journal of Chemical Information and Computer Sciences, 35, 53-58.
R Development Core Team (2009). R: a Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing. (
Smith, E., Lebrun, A., Labella, R. (2013). Potential Roles for Unattended Safeguards Instrumentation at Centrifuge Enrichment Plants, Journal of Nuclear Materials Management 32(1), 38-58.
Speed, T., Culpin D. (1986). The Role of Statistics in Nuclear Materials Accounting: Issues and Problems, Journal of the Royal Statistical Society A, 149(4), 281-313. 1986.
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