Program - Brookhaven National Laboratory

former case, more realistic covariance matrices are established in colloboration with experimentalists using
detailed experimental information, see e.g. [1]. In the latter case, emphasis is put on the quantification of
model deficiencies, see [2]. The impact of these advances is discussed by means of an evaluation of Np-237
and by prior data of Np-236.
[1] “Covariance matrix for a relative Np237 (n,f) cross section measurement,” F.Tovesson, T.S.Hill, K.M.Hanson,
P.Talou, T.Kawano, R.C.Haight, and L.Bonneau, LA-UR-06-7318 (2006) [2] “Consistent procedure for
nuclear data evaluation based on modelling,” H. Leeb, D. Neudecker, Th. Srdinko. Nuclear Data Sheets
2762, 109 (2008)
FC 3 11:20 AM
Uncertainty Quantification of Prompt Fission Neutron Spectra using the Unified Monte
Carlo Method
M.E. Rising, P. Talou
Theoretical Division, Los Alamos National Laboratory, USA
A.K. Prinja
Chemical and Nuclear Engineering Department, University of New Mexico, USA
In the ENDF/B-VII.1 nuclear data library [1], the existing covariance evaluations of the prompt fission
neutron spectra (PFNS) were derived by combining experimental differential data where available with
theoretical model calculations, relying on the use of a first-order linear Bayesian approach, the Kalman
filter [2]. This approach requires in particular that the theoretical model response to changes in input
parameters be linear about the prior central values. If the model response is nonlinear, the Kalman filter
may lead to an inaccurate evaluation of the PFNS and associated uncertainties. One possible remedy to
the issues associated with the first-order linear Kalman filter is the use of the so-called Unified Monte
Carlo (UMC) approach [3]. The UMC method remains a Bayesian approach where the probability density
functions (PDFs) of the a priori and the likelihood must be known to determine the PDF of the a posteriori.
Similar to the Kalman filter approach, the Principle of Maximum Entropy is employed and the shape of
the a priori and likelihood PDFs are chosen to be multivariate Gaussian distributions. Now, before any
assumptions are made, according to Bayes’ theorem, the unnormalized a posteriori PDF is formed as the
product of the a priori and likelihood PDFs. The UMC approach samples directly from the a posteriori
PDF and as the number of samples increases, the statistical noise in the computed a posteriori moments
converge to an appropriate solution which corresponds to the true mean of the underlying a posteriori PDF.
Recently, the UMC approach has been studied in the context of comparing the convergence properties of
differing Monte Carlo sampling techniques. We have implemented the UMC approach for the evaluations
of the PFNS and its associated uncertainties and compared the results to the tradition first-order linear
Kalman filter approach. The brute force Monte Carlo approach has been implemented with success but
with an obvious computational disadvantage compared with the Kalman filter approach. Other methods
that help improve the computational limitations of the UMC approach, including the stochastic collocation
method (SCM), are studied in the framework of the UMC approach and these results will be presented.
These results may help demonstrate what impact the UMC evaluation methodology can have on future
evaluations of important nuclear data.
[1] M.B. CHADWICK, M. HERMAN, P. OBLOZINSKY et al., “ENDF/B-VII.1 Nuclear Data for Science
and Technology: Cross Sections, Covariances, Fission Product Yields and Decay Data,” Nuclear Data
Sheets, 112, 2887 (2011). [2] R.E. KALMAN, “A New Approach to Linear Filtering and Prediction
Problems”, J. Basic Eng., 82D, 35-45 (1960). [3] R. CAPOTE and D.L. SMITH, “An Investigation of the
Performance of the Unified Monte Carlo Method of Neutron Cross Section Data Evaluation”, Nucl. Data
Sheets, 109 (12), 2768 (2008).
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