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.