On the Methodology to Calculate the Covariance of Estimated Resonance Parameters

Abstract

Principles to determine resonance parameters and their covariance from experimental data are discussed. Different methods to propagate the covariance of experimental parameters are compared. A full Bayesian statistical analysis reveals that the level to which the initial uncertainty of the experimental parameters propagates, strongly depends on the experimental conditions. For high precision data the initial uncertainties of experimental parameters, like a normalization factor, has almost no impact on the covariance of the parameters in case of thick sample measurements and conventional uncertainty propagation or full Bayesian analysis. The covariances derived from a full Bayesian analysis and least-squares fit are derived under the condition that the model describing the experimental observables is perfect. When the quality of the model can not be verified a more conservative method based on a renormalization of the covariance matrix is recommended to propagate fully the uncertainty of experimental systematic effects. Finally, neutron resonance transmission analysis is proposed as an accurate method to validate evaluated data libraries in the resolved resonance region.