Theoretical and Practical Study of the Variance and Efficiencyof a Monte Carlo calculation due to Russian roulette

摘要

Although Russian roulette is applied very often in Monte Carlorncalculations, not much literature exists on its quantitative influence on thernvariance and efficiency of a Monte Carlo calculation. Elaborating on thernwork of Lux and Koblinger using moment equations, new relevant equationsrnare derived to calculate the variance of a Monte Carlo simulation usingrnRussian roulette. To demonstrate its practical application the theory isrnapplied to a simplified transport model resulting in explicit analyticalrnexpressions for the variance of a Monte Carlo calculation and for thernexpected number of collisions per history. From these expressionsrnnumerical results are shown and compared with actual Monte Carlorncalculations, showing an excellent agreement. By considering the numberrnof collisions in a Monte Carlo calculation as a measure of the CPU time,rnalso the efficiency of the Russian roulette can be studied. It opens the wayrnfor further investigations, including optimization of Russian rouletternparameters.