Variance Reduction MCMs with Application in Environmental Studies: Sensitivity Analysis

This paper studies generator sensitivity of some variance reduction Monte Carlo methods (MCMs) with acceptance-rejection for approximate calculation of multiple integrals. This investigation is important basis for the development of the grid application Monte Carlo Sensitivity Analysis for Environmental Systems in the framework of the SEE-GRID-SCI project. Monte Carlo are among the most widely used methods in real simulations. These methods can be considered as methods for computing an integral in the unit cube of an appropriate dimension, called the constructive dimensionality of the method. Since its worst-case convergence rate of O(N-1/2) does not depend on the dimension of the integral, Monte Carlo is sometimes the only viable method for a wide range of high-dimensional problems. Many studies show that the outcome of the simulation may be sensitive to the random generators being used, which means that obtaining unbiased estimates requires careful selection of the random generators. The random number generators based on physical events present an important option in this regard. In this paper we study the sensitivity of several variance reduction Monte Carlo methods: importance sampling, smoothed importance sampling, weighted uniform sampling and crude Monte Carlo, to different type of generators: Quantum Random Bit Generator, pseudorandom generators and quasi-random sequences. Extensive numerical tests of several test integrals are presented.