Lognormal Bayesian estimation of fission product yield covariance matrix

Covariance matrix of fission product yields (FPYs) is important in propagating FPYs' uncertainty to burnup calculation of reactors, however, it is absent in the current release of ENDF/B-VII.1. Bayesian updating method is used to estimate this covariance matrix from the physical constraints among FPYs. Conventional normal Bayesian method adopts normal distribution to describe FPY probability density, which violates FPYs’ inherent positive physical nature. In order to tackle such issue, lognormal Bayesian method is introduced in this work and FPYs from thermal neutron induced U-235 fission system are considered. By comparing between normal and lognormal Bayesian estimated covariance matrices, it is found that large relative difference (larger than 30%) is observed in the updated FPY standard deviations. Lognormal Bayesian method would preserve the non-negativity of FPY. This would further constraint the estimated strong anti-correlations among FPYs compared with normal Bayesian method. From this work, it is suggested that the non-negativity of FPY should be underlined in FPY covariance matrix estimation process. And lognormal Bayesian method should be used in FPY covariance estimation because of its mathematical self-consistency in preserving the non-negativity of FPYs.