Statistical error methods in computer simulations
Two methods of studying the statistical error in sequences of data obtained by computer simulation when the data series is strongly correlated are compared. The first method divides the series into a number of subseries whose length is selected graphically by means of the ``statistical inefficiency'' (SI). The SI is defined as the limiting ratio of the observed variance of the subseries averages to their expected (Gaussian) variance. Different algorithms are given for choosing the appropriate number of subseries. The second method uses the autocorrelation function of all the values obtained and analytically calculates its convergence by means of the ``correlation length'' \(\tau\). The general relationship \(SI=1+2\tau\) between the two parameters SI and \(\tau\) is found mathematically and is in good agreement with the experimental data obtained by molecular dynamics simulation in the melting zone where the correlations have a long-rage trend when a very accurate algorithm is used. As a consequence, the analytical method is more accurate than the graphical method. The conclusions about the concordance between the theoretical result and experimental results are shown. Both statistical methods of estimating the statistical error in the data series have the advantage that they can be applied to data from any kind of simulation, molecular dynamics or Monte Carlo. These methods permit to determine whether or not there exists a correlation between the values obtained.
scientific article; zbMATH DE number 4190974