Maximum likelihood estimators and extreme value theory for uncertainty quantification in criticality analysis

Uncertainty quantification is an important topic in criticality analysis. In this paper two approaches are investigated, one based on the use of Maximum Likelihood estimators for the estimation of bias in calculations and one based on Extreme Value Theory which is investigated in the context of assessing tolerance limits on k_eff. The Maximum Likelihood estimator is a very general approach, and here single and multiple parameter models are investigated for both continuous and discrete parameters. The discrete parameter case can be related to groups of experiments which share common apparatus, which could lead to correlations in the experimental bias. The statistical models and their results are compared with linear regression models where appropriate. The Extreme Value Theory approach is applied to a simple model, and the method is compared against the commonly-used Wilks approach. (authors)