Physics – Data Analysis – Statistics and Probability
Scientific paper
2012-04-14
Physics
Data Analysis, Statistics and Probability
{\em Journal of Computational Physics}, submitted, 2012
Scientific paper
In Monte Carlo simulations, the thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples. As the stochastic error of the simulation results is significant, it is desirable to understand the variance of the estimation by ensemble average, which depends on the sample size (i.e., the total number of samples in the set) and the sampling interval (i.e., cycle number between two consecutive samples). Although large sample sizes reduce the stochastic error, they increase the computational cost of the simulation. In this work, we report a few general rules that relate the variance with the sample size and the sampling interval. These relations were observed in our numerical results. The main contribution of this work is the theoretical proof of these numerical observations and the set of assumptions that lead to them.
Calo Victor M.
Li Jiying
Sun Sam-Shajing
Vignal P.
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