Prediction of Statistical Error and Optimization of Biased Monte Carlo Transport Calculations

Integral equations are derived to provide the expected statistical error in any biased Monte Carlo transport calculation. The equations result from a generalization of a recent formulation by Amster and Djomehri. The present treatment is general enough to handle situations where more than one particle emerge from a collision with distribution in the statistical weights. These formulations have been used to obtain the variance and the number of collisions per history in a few Monte Carlo schemes using exponential transform. The schemes considered include procedures such as splitting, weighting in lieu of absorption, and next-event estimation. Optimization of different procedures as well as their comparative merits are discussed for a sample one-group problem.