A non-parametric bootstrap method for Monte Carlo neutron transport

Abstract

A new variability inference technique for Monte Carlo transport methods has been investigated. This approach is based on non-parametric bootstrapping, a statistical inference and resampling method in which an observed set of samples is used to generate simulated samples to infer statistical properties of the underlying distribution from which the original samples were drawn. In this way, non-parametric bootstrapping can be applied to estimators to quantify the uncertainty of the corresponding estimates as well as any bias introduced by bootstrapping, which can then be used to correct the bias. In this context, we have used non-parametric bootstrapping to estimate the first and second-order moments of estimations of Monte Carlo integral responses for different neutron transport problems. This was implemented in SCONE — Stochastic Calculator Of Neutron transport Equation, developed at the University of Cambridge. Results show that the non-parametric bootstrap method can improve the efficiency of the estimates, that is, achieve a favourable trade-off between simulation time and variance of integral response estimates while being more accurate, compared to standard MC estimates. This is particularly the case for low sample sizes and when the number of responses is kept to a moderate level, which is expected according to the underlying theory which has been investigated. As the number of responses increases, however, challenges with bias, memory and computational efficiency become more prominent, which is addressed.