TITLE:
History-by-History Variance in Monte Carlo Simulation of Radiation Interactions with Matter
AUTHORS:
Mary Pik Wai Chin
KEYWORDS:
Monte Carlo, FLUKA, Error, Statistics, Variance
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.3,
March
21,
2017
ABSTRACT: Radiation interaction with matter is by nature stochastic. Monte Carlo simulation makes possible, practical, economical and ethical, many experiments otherwise not. In-silico simulation of random samples of radiation histories places into our hands data which may be treated and analysed in radically different ways. This work reports history-by-history computation of the variance in simulation output from FLUKA, a general-purpose Monte Carlo code. Variance computed history by history is compared with variance estimated from varying batch sizes. This work also addresses the issue of under-sampling where, against conventional expectations, the variance spikes as we sample more histories. The background to the spikes is traced by reconstructing single histories interaction by interaction—a novel level of details atypical of Monte Carlo simulations in the field, where statistical convergence of averaged quantities has been the focus.