How confident can we be in confidence intervals for the computational bias obtained with the generalized linear least squares methodology? - A toy model analysis - 5-11

The so-called Generalized Linear Least Squares Methodology (GLLSM) is widely used for estimating the computational bias Δk of the neutron multiplication factor k and its uncertainty. Although mathematically consistent, the GLLSM is based on assumptions. In particular, uncertainties in k are assumed to be governed by covariances of the given nuclear data evaluation α* , i.e. errors due to shortcomings in the transport code and due to nuclear data processing are neglected. Furthermore, differences between α* and the true nuclear data α are assumed to be sufficiently small for k(α) to be approximated by a first order series expansion about α* . Since one might be doubtful about the validity of the GLLSM assumptions, a toy model analysis is performed to study the impact of their violation on the coverage probability of GLLSM confidence intervals for Δk. For each of the analyzed cases, a large number of Monte Carlo samples of α* and benchmark k values is drawn, and the fraction of times Δk is covered by a GLLSM confidence interval is compared to its alleged confidence level. Among other results, we find that the deviation between alleged and true confidence level can be considerable for nuclear data uncertainties larger than 1%. Hence, using the GLLSM may result in a serious underestimation of the Δk uncertainty. (authors)