Universal Methodology for Statistical Error and Convergence of Correlated Monte Carlo Tallies

It is known that the convergence of standardized time series (STS) to Brownian bridge yields standard deviation estimators of the sample mean of correlated Monte Carlo tallies. In this work, a difference scheme based on a stochastic differential equation is applied to STS in order to obtain a new functional statistic (NFS) that converges to Brownian motion (BM). As a result, statistical error estimation improves twofold. First, the application of orthonormal weighting to NFS yields a new set of asymptotically unbiased standard deviation estimators of sample mean. It is not necessary to store tallies once the updating of estimator computation is finished at each generation. Second, it becomes possible to assess the convergence of sample mean in an assumption-free manner by way of the comparison of power spectra of NFS and BM. The methodology is demonstrated for a challenging criticality problem based on Mennerdahl’s work, reactor tallies of representative correlation characteristics, and the delayed neutron fraction calculation of units of loosely coupled highly enriched uranium and ²³⁹Pu.