Doctoral Dissertations
Date of Award
12-1989
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Nuclear Engineering
Major Professor
Paul N. Stevens
Abstract
Various techniques devised to flag undersampling conditions were investigated. Undersampling conditions can often lead to underestimation and a solution which can be significantly smaller than the true solution but the estimate of the standard deviation may seem acceptably small. In an attempt to identify undersampling in Monte Carlo calculations, the estimation of F values, the coefficient of variation of the standard deviation, the figure of merit, and a particle contribution distribution histogram were incorporated into the MORSE code.
It was found for the problems considered that the F tests were not conclusive because the distribution of contributions was not normally distributed. The calculation of the coefficient of variation turned out to require significantly more computational effort than that necessary to directly achieve a very small standard deviation because of its dependency upon the kurtosis of the distribution which takes much longer than the variance to achieve a stable value. If the kurtosis is not too large, this coefficient can be used in problems which demand high degrees of precision such as criticality calculations.
The figure of merit FOM = 1/σ2t is a function of the variance of the population which becomes stable faster than its coefficient of variation. Therefore, the FOM provides a more reliable guarantee of a stable solution - also, because it tends to a constant value, it is more easily analyzed. However, in severe undersampling conditions the FOM may become apparently constant over a large range of sample sizes and then abruptly changing with the sampling of rare particles. Also, a sudden increase in the variance may not have an accompanying significant change in the mean while the figure of merit experiences a jump. Under this condition, the solution may still be a perfectly acceptable estimate.
The creation of the particle contribution distribution which is output at the end of each batch provides a very effective way of detecting undersampling. If only a few particles account for a large fraction of the response, the estimates of both mean and standard deviation should be regarded as unreliable and, therefore, the sample size should be increased.
Although not thoroughly investigated, the utilization of the statistical tools implemented into the MORSE code was demonstrated to be useful in the study of the behavior of particle distributions when subjected to various biasing and/or estimation procedures.
Recommended Citation
Vieria, Wilson José, "A general study of undersampling problems in Monte Carlo calculations. " PhD diss., University of Tennessee, 1989.
https://trace.tennessee.edu/utk_graddiss/11783
