Estimation of Population Variance in Contributon Monte Carlo

Based on the theory of contributions, a new Monte Carlo method known as the contributon Monte Carlo method has recently been developed. The method has found applications in several practical shielding problems. We analyze theoretically the variance and efficiency of the new method, by taking moments around the score. In order to compare the contributon game with a game of simple geometrical splitting and also to get the optimal placement of the contributon volume, the moments equations were solved numerically for a one-dimensional, one-group problem using a 10-mfp-thick homogeneous slab. It is found that the optimal placement of the contributon volume is adjacent to the detector; even at its most optimal the contributon Monte Carlo is less efficient than geometrical splitting.