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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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Volume 19, Issue 1


A direct inversion method for non-uniform quasi-random point sequences

Colas Schretter / Harald Niederreiter
Published Online: 2013-03-06 | DOI: https://doi.org/10.1515/mcma-2012-0014


The inversion method is an effective approach for transforming uniform random points according to a given probability density function. In two dimensions, horizontal and vertical displacements are computed successively using a marginal and then all conditional density functions. When quasi-random low-discrepancy points are provided as input, spurious artifacts might appear if the density function is not separable. Therefore, this paper relies on combining intrinsic properties of the golden ratio sequence and the Hilbert space filling curve for generating non-uniform point sequences using a single step inversion method. Experiments show that this approach improves efficiency while avoiding artifacts for general discrete probability density functions.

Keywords: Quasi-random points; non-uniform distribution; inversion method; golden ratio sequence; van der Corput sequence

About the article

Received: 2012-06-11

Accepted: 2012-11-15

Published Online: 2013-03-06

Published in Print: 2013-03-01

Citation Information: Monte Carlo Methods and Applications, Volume 19, Issue 1, Pages 1–9, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma-2012-0014.

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