Variance Reduction with Multiple Responses

Radiation transport problems that involve high attenuation require non-analogue Monte Carlo. Non-analogue techniques (i.e. employing variance reduction (V.R.) ), conserve the first moment whilst reducing the second and consequently the variance. However, because V.R. methods employ in one form or another an estimate of the importance (adjoint flux) which is strictly linked to a particular response, they are directed at a single response. V.R. parameters appropriate to one response (in that they significantly reduce the statistical error) may not necessarily be appropriate to another; they may even raise the errors of other responses compared with their analogue values. Thus Monte Carlo may treat problems involving a high attenuation only if a single response (or a set of responses with similar importances) is of interest. Monte Carlo tends to run into trouble when more differential information is required (flux distributions in many energy groups for example). The technique presented here to optimize V.R. parameters to more than one response is based on the DSA (Direct Statistical Approach) which is of general application in that it is based on V.R. techniques that are themselves of general use: population or weight control through splitting and Russian roulette.