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Adaptive Quasi-Monte Carlo Integration Based on MISER and VEGAS

In: Monte Carlo and Quasi-Monte Carlo Methods 2002

Author

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  • Rudolf Schürer

    (University of Salzburg, Department of Mathematics)

Abstract

Summary Quasi-Monte Carlo (QMC) routines are one of the most common techniques for solving integration problems in high dimensions. However, their efficiency degrades if the variation of the integrand is concentrated in small areas of the integration domain. Adaptive algorithms cope with this situation by adjusting the flow of computation based on previous integrand evaluations. We explore ways to modify the Monte Carlo based adaptive algorithms MISER and VEGAS such that low-discrepancy point sets are used instead of random samples. Experimental results show that the proposed algorithms outperform plain QMC as well as the original adaptive integration routine for certain classes of test cases.

Suggested Citation

  • Rudolf Schürer, 2004. "Adaptive Quasi-Monte Carlo Integration Based on MISER and VEGAS," Springer Books, in: Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2002, pages 393-406, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18743-8_25
    DOI: 10.1007/978-3-642-18743-8_25
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