Algorithmic Refinements for Multicanonical System Measurements

We have adapted, to our knowledge for the first time, multicanonical sampling and its Wang-Landau extension to the analysis of the statistics of communication systems, and by extension, arbitrary stochastic physical systems.[D. Yevick, ``A First Course in Computational Physics and Object Oriented Programming with C++``, Cambridge University Press, Ch. 22 and references] Subsequently, we applied the technique experimentally with and without a novel biasing procedure for the intermediate pdf distributions that significantly enhances the statistics in selected regions of system variables. [T. Lu, D. Yevick et. al.\textbf{,} IEEE Photon. Technol. Lett, \textbf{17}, 1420 (2005) and to be published]. Here we additionally discuss procedures that (1) bias the statistical samples by raising the estimated pdf to a power (2) combine intermediate results in a manner identical to that employed in importance sampling (3) incorporate non-uniform Markov chain displacements and (4) interpolate the histogram and pdf values during iterations. These significantly impact experiments with a restricted number of samples.[D. Yevick et. al., submitted to J. Opt. Soc. Am. A]