A Systematic Description of the Generation of Covariance Matrices

Although the importance of covariances has been recognized by the nuclear community, there appears to be limited understanding of the nature of covariances and the manner in which they contribute to the solution of physical problems. This paper is an attempt to provide a systematic description of the various sources of uncertainty, their contributions to covariance matrices (CMs), and the effect they may have on the calculated values and uncertainties of integral quantities such as keff. Our intent is to elucidate some important, but often overlooked, properties of CMs. First, one must recognize that the set of quantities (data, parameters, etc.) associated with the CM must be specified in order for the term “covariance matrix ” to be meaningful. For example, the CM associated with the energy-differential experimental cross section provides a measure of the uncertainty on each individual data point (cross section at a particular energy) and of the relationship (correlation) between those data points. In this paper, we discuss the various techniques used to determine realistic and appropriate CMs associated with quantities of interest at the many different stages of nuclear data processing, starting from measurement of energy-differential neutron cross sections through the final calculation