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New Inputs and Methods for Markov Chain Quasi-Monte Carlo

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Monte Carlo and Quasi-Monte Carlo Methods 2010

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 23))

Abstract

We present some new results on incorporating quasi-Monte Carlo rules into Markov chain Monte Carlo. First, we present some new constructions of points, fully equidistributed LFSRs, which are small enough that the entire point set can be used in a Monte Carlo calculation. Second, we introduce some antithetic and round trip sampling constructions and show that they preserve the completely uniformly distributed property necessary for QMC in MCMC. Finally, we also give some new empirical results. We see large improvements in sampling some GARCH and stochastic volatility models.

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Acknowledgements

This work was supported by grant DMS-0906056 from the U.S. National Science Foundation and by JSPS Grant-in-Aid for Scientific Research No.19204002, No.21654017, No.23244002 and JSPS Core-to-Core Program No.18005. We thank the organizers of MCQMC 2010, Leszek Pleskota and Henryk Woźniakowski, for providing an excellent scientific venue.

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Authors and Affiliations

  1. Stanford University, Stanford, CA, USA

    Su Chen & Art B. Owen

  2. University of Tokyo, Tokyo, Japan

    Makoto Matsumoto

  3. Yamagata University, Yamagata, Japan

    Takuji Nishimura

Authors
  1. Su Chen
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  2. Makoto Matsumoto
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  3. Takuji Nishimura
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  4. Art B. Owen
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Corresponding author

Correspondence to Su Chen .

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Editors and Affiliations

  1. , Institute of Applied Mathematics, University of Warsaw, Banacha 2, Warsaw, 02-097, Poland

    Leszek Plaskota

  2. , Institute of Applied Mathematics, University of Warsaw, Banacha 2, Warsaw, 02-097, Poland

    Henryk Woźniakowski

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Chen, S., Matsumoto, M., Nishimura, T., Owen, A.B. (2012). New Inputs and Methods for Markov Chain Quasi-Monte Carlo. In: Plaskota, L., Woźniakowski, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2010. Springer Proceedings in Mathematics & Statistics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27440-4_15

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