Statistical Errors in Biasing Monte Carlo Simulations With Applications to Polarization-Mode Dispersion Compensators

Abstract

The possible sources of error in Monte Carlo (MC) simulations are errors in physical modeling, coding errors (bugs), statistical errors, and algorithmic errors. While most algorithmic errors lead to large statistical errors, subtle algorithmic errors that do not lead to statistical errors are at least theoretically possible. These sources of error are reviewed, with the emphasis on statistical errors. Methods for calculating the statistical error in two types of biasing MC simulation, i.e., 1) standard importance sampling and 2) multicanonical, are described. The former requires a priori knowledge of how to bias the simulation, while the latter does not. Examples are drawn from the work of the author and his colleagues on calculating the effects of polarization-mode dispersion in optical fiber communication systems. Potential pitfalls when MC simulation codes are not carefully validated and statistical errors are not carefully monitored are described. A proposal for best practice in which statistical errors are always presented in conjunction with MC simulations is made