Error estimation in multicanonical Monte Carlo simulations with applications to polarization-mode-dispersion emulators

This paper shows how to estimate errors in multi-canonical Monte Carlo (MMC) simulations using a transition-matrix method. MMC is a biasing Monte Carlo technique that allows one to compute the probability of rare events, such as the outage probability in optical-fiber communication systems. Since MMC is a Monte Carlo technique, it is subject to statistical errors, and it is essential to determine their magnitude. Since MMC is a highly nonlinear iterative method, linearized error-propagation techniques and standard error analyses do not work, and a more sophisticated method is needed. The proposed method is based on bootstrap techniques. This method was applied to efficiently estimate the error in the probability density function (pdf) of the differential group delay (DGD) of polarization-mode-dispersion (PMD) emulators that has been calculated using MMC. The method was validated by comparison to the results obtained using a large ensemble of MMC simulations.