Cross-section adjustment methods based on minimum variance unbiased estimation

ABSTRACT

On the basis of the minimum variance approach, the unified formulation for three types of the cross-section adjustment methods has been derived in a straightforward way without assuming the normal distribution. These methods are intended to minimize the variances of the predicted target core parameters, the adjusted cross-section set, and the calculated integral experimental values. The first and the second methods are found to be slightly different from the extended and the conventional cross-section adjustment methods based on the Bayesian approach with the normal distribution assumption, respectively. However, they become equivalent in some cases and results. The third method is a new method, which is necessary from the viewpoint of the symmetry of the formulation. In addition, it is verified by numerical calculations that the derived formulation gives the minimized variances as intended. The derivation procedure proposed in the present paper is potentially applicable to developing more sophisticated cross-section adjustment methods because of the less assumptions on the probability density function.

Keywords:

• Cross-section adjustment
• minimum variance unbiased estimation
• maximum likelihood estimation
• Bayes’ theorem
• normal distribution
• uncertainty
• covariance

Acknowledgements

K. Yokoyama wishes to express his deep gratitude to Mr M. Ishikawa of the Japan Atomic Energy Agency for providing useful comments on this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.