Zero Variance Penalty Model for the Generation of Covariance Matrices in Integral Data Assimilation Problems

This paper presents simple models developed to generate covariances between observable and latent variables. The methodology consists of using “variance penalty” terms as a measure of the contribution of the latent-variable uncertainties to the variance of a given calculated quantity z. This approach provides a useful understanding of how the observable and latent variables are related to each other and ensures the positive-definiteness of the covariance matrix. This work has been implemented in the nuclear data assimilation tool CONRAD. Performances of analytic and Monte Carlo models are illustrated with covariances calculated for neutron-induced capture reactions on stable xenon isotopes (¹²⁴Xe, ¹²⁶Xe, ¹²⁸Xe, ¹²⁹Xe, ¹³⁰Xe, ¹³²Xe, and ¹³⁴Xe).