Biases in Monte Carlo Eigenvalue Calculations

The derivation of the standard expression for the Monte Carlo eigenvalue bias is reviewed. It is noted that the bias is due to the repeated normalization of the fission source by the eigenvalue. This normalization can be partially or completely eliminated, but when this is done, the variance in the eigenvalue may increase unacceptably. Thus, it seems impractical, in general, to eliminate the bias in this way. Next, the Brissenden-Garlick relation between eigenvalue bias and variance is rederived for nonanalog tracking and estimation. From this relation, it is shown that the eigenvalue bias under “normal conditions is smaller than the eigenvalue’s standard deviation. In this sense, the bias is not significant, so that it is not crucially important to eliminate or to estimate it.