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- Helgesson, Petter, 1986-, et al.
(författare)
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Combining Total Monte Carlo and Unified Monte Carlo : Bayesian nuclear data uncertainty quantification from auto-generated experimental covariances
- 2017
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Ingår i: Progress in nuclear energy (New series). - : Elsevier. - 0149-1970 .- 1878-4224. ; 96, s. 76-96
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Tidskriftsartikel (refereegranskat)abstract
- The Total Monte Carlo methodology (TMC) for nuclear data (ND) uncertainty propagation has been subject to some critique because the nuclear reaction parameters are sampled from distributions which have not been rigorously determined from experimental data. In this study, it is thoroughly explained how TMC and Unified Monte Carlo-B (UMC-B) are combined to include experimental data in TMC. Random ND files are weighted with likelihood function values computed by comparing the ND files to experimental data, using experimental covariance matrices generated from information in the experimental database EXFOR and a set of simple rules. A proof that such weights give a consistent implementation of Bayes' theorem is provided. The impact of the weights is mainly studied for a set of integral systems/applications, e.g., a set of shielding fuel assemblies which shall prevent aging of the pressure vessels of the Swedish nuclear reactors Ringhals 3 and 4.In this implementation, the impact from the weighting is small for many of the applications. In some cases, this can be explained by the fact that the distributions used as priors are too narrow to be valid as such. Another possible explanation is that the integral systems are highly sensitive to resonance parameters, which effectively are not treated in this work. In other cases, only a very small number of files get significantly large weights, i.e., the region of interest is poorly resolved. This convergence issue can be due to the parameter distributions used as priors or model defects, for example.Further, some parameters used in the rules for the EXFOR interpretation have been varied. The observed impact from varying one parameter at a time is not very strong. This can partially be due to the general insensitivity to the weights seen for many applications, and there can be strong interaction effects. The automatic treatment of outliers has a quite large impact, however.To approach more justified ND uncertainties, the rules for the EXFOR interpretation shall be further discussed and developed, in particular the rules for rejecting outliers, and random ND files that are intended to describe prior distributions shall be generated. Further, model defects need to be treated.
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| 2. |
- Helgesson, Petter, 1986-, et al.
(författare)
-
Sampling of systematic errors to estimate likelihood weights in nuclear data uncertainty propagation
- 2016
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Ingår i: Nuclear Instruments and Methods in Physics Research Section A. - : Elsevier. - 0168-9002 .- 1872-9576. ; 807, s. 137-149
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Tidskriftsartikel (refereegranskat)abstract
- In methodologies for nuclear data (ND) uncertainty assessment and propagation based on random sampling, likelihood weights can be used to infer experimental information into the distributions for the ND. As the included number of correlated experimental points grows large, the computational time for the matrix inversion involved in obtaining the likelihood can become a practical problem. There are also other problems related to the conventional computation of the likelihood, e.g., the assumption that all experimental uncertainties are Gaussian. In this study, a way to estimate the likelihood which avoids matrix inversion is investigated; instead, the experimental correlations are included by sampling of systematic errors. It is shown that the model underlying the sampling methodology (using univariate normal distributions for random and systematic errors) implies a multivariate Gaussian for the experimental points (i.e., the conventional model). It is also shown that the likelihood estimates obtained through sampling of systematic errors approach the likelihood obtained with matrix inversion as the sample size for the systematic errors grows large. In studied practical cases, it is seen that the estimates for the likelihood weights converge impractically slowly with the sample size, compared to matrix inversion. The computational time is estimated to be greater than for matrix inversion in cases with more experimental points, too. Hence, the sampling of systematic errors has little potential to compete with matrix inversion in cases where the latter is applicable. Nevertheless, the underlying model and the likelihood estimates can be easier to intuitively interpret than the conventional model and the likelihood function involving the inverted covariance matrix. Therefore, this work can both have pedagogical value and be used to help motivating the conventional assumption of a multivariate Gaussian for experimental data. The sampling of systematic errors could also be used in cases where the experimental uncertainties are not Gaussian, and for other purposes than to compute the likelihood, e.g., to produce random experimental data sets for a more direct use in ND evaluation.
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