A new method of assessing the statistical convergence of Monte Carlo solutions

Accurate Monte Carlo confidence intervals (CIs), which are formed with an estimated standard deviation, can only be created when the number of particle histories N becomes large enough so that the central limit theorem can be applied. The Monte Carlo user has a limited number of marginal methods to assess the fulfillment of this condition, such as statistical error reduction proportional to 1/√N with error magnitude guidelines and third and fourth moment estimators. A new method is presented in this paper to asses the statistical convergence of Monte Carlo solutions by analyzing the shape of the empirical probability density function (pdf) of history scores. Related work in this area includes the derivation of analytic score distributions for a two-state Monte Carlo problem. Score distribution histograms have been generated to determine when a small number of histories accounts for a large fraction of the result. This paper describes initial studies of empirical Monte Carlo history score pdf's created from score histograms of particle transport simulations