Exploring pseudo- and chaotic random Monte Carlo simulations

Authors:
J.A. Rod Blais;Zhan Zhang
Affiliations:
Department of Geomatics Engineering, Pacific Institute for the Mathematical Sciences, University of Calgary, Calgary, AB, Canada T2N 1N4;Department of Geomatics Engineering, Pacific Institute for the Mathematical Sciences, University of Calgary, Calgary, AB, Canada T2N 1N4
Venue:
Computers & Geosciences
Year:
2011

Citing 3
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HPCN Europe 2000 Proceedings of the 8th International Conference on High-Performance Computing and Networking

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Abstract

Computer simulations are an increasingly important area of geoscience research and development. At the core of stochastic or Monte Carlo simulations are the random number sequences that are assumed to be distributed with specific characteristics. Computer-generated random numbers, uniformly distributed on (0, 1), can be very different depending on the selection of pseudo-random number (PRN) or chaotic random number (CRN) generators. In the evaluation of some definite integrals, the resulting error variances can even be of different orders of magnitude. Furthermore, practical techniques for variance reduction such as importance sampling and stratified sampling can be applied in most Monte Carlo simulations and significantly improve the results. A comparative analysis of these strategies has been carried out for computational applications in planar and spatial contexts. Based on these experiments, and on some practical examples of geodetic direct and inverse problems, conclusions and recommendations concerning their performance and general applicability are included.