On The Accuracy Of keff Estimated By Monte Carlo Method

Monte Carlo methods used to estimate eigenvalues (keff) of multiplying systems are inherently non-ergodic studies of a stochastic branching process. We develop theoretical distributions for keff and compare them with Monte Carlo results for sub-, super- and critical systems with no internal distributions in the expectation that all such studies will have the same essential behaviour. Comparing arithmetic and geometric averages of keff we find that. over a few generations at any rate, sub-critical systems can be more accurately assessed by using geometric average. If a certain number of generations is to be discarded to let the system settle, then it is shown that an optimisation of computation calls for more generations to be studied and smaller initial samples