Comparison of theoretical formulae and bootstrap method for statistical error estimation of Feynman-α method

• Published in: Annals of nuclear energy 2019-02, Vol.124, p.606-615
• Main Authors: Endo, Tomohiro, Yamamoto, Akio
• Format: Article
• Language: English
• Subjects: Bootstrap method; Covariance; Feynman-α method; Prompt neutron decay constant; Statistical error
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/j.anucene.2018.10.032

•Estimation formulae for statistical error of variance-to-mean ratio Y are derived.•Statistical error of Y can be estimated by reusing Y without higher-order moments.•Bootstrap method enables covariance estimation of Y between counting gate widths.•Covariance is useful in better error-estimation of prompt neutron decay constant. This paper discusses the statistical error of the variance-to-mean ratio, or the Y value in the Feynman-α method, from a single measurement of reactor noise. As a theoretical approach, two practical theoretical formulae are derived to estimate the statistical error of Y: one is based on the propagation of uncertainty with unbiased estimators for the third- and fourth-order central moments; the other is a simplified formula that reuses the Y value under the fundamental mode approximation, where the subcriticality is approximately less than 10,000 pcm. As a numerical approach, the bootstrap method is improved to efficiently estimate the correlations of Y between different counting gate widths, or covariance matrix ΣY, due to the bunching method. Through an actual reactor noise experiment at the Kyoto University Criticality Assembly, the statistical errors of Y using the theoretical formulae and the bootstrap method are validated by comparing the reference statistical errors that are estimated from the multiple experiments of reactor noise. Furthermore, the impact of ΣY on the statistical error of the prompt neutron decay constant α is numerically investigated. Consequently, in the case of this experimental analysis, it was confirmed that the bootstrap method with the correlations of Y seems to be slightly better from the viewpoint of the coverage probability of the estimated confidence intervals of α, although the fitting error method without the correlation of Y could be useful for the order estimation of the statistical error of α.