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Variance reduction for diffusions

Author

Listed:
  • Hwang, Chii-Ruey
  • Normand, Raoul
  • Wu, Sheng-Jhih

Abstract

The most common way to sample from a probability distribution is to use Markov Chain Monte Carlo methods. One can find many diffusions with the target distribution as equilibrium measure, so that the state of the diffusion after a long time provides a good sample from that distribution. One naturally wants to choose the best algorithm. One way to do this is to consider a reversible diffusion, and add to it an antisymmetric drift which preserves the invariant measure. We prove that, in general, adding an antisymmetric drift reduces the asymptotic variance, and provide some extensions of this result.

Suggested Citation

  • Hwang, Chii-Ruey & Normand, Raoul & Wu, Sheng-Jhih, 2015. "Variance reduction for diffusions," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3522-3540.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:9:p:3522-3540
    DOI: 10.1016/j.spa.2015.03.006
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    References listed on IDEAS

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    1. Mira, Antonietta, 2001. "Efficiency of finite state space Monte Carlo Markov chains," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 405-411, October.
    2. Pai, Hui-Ming & Hwang, Chii-Ruey, 2013. "Accelerating Brownian motion on N-torus," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1443-1447.
    3. Chen, Ting-Li & Hwang, Chii-Ruey, 2013. "Accelerating reversible Markov chains," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 1956-1962.
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    Cited by:

    1. Belmabrouk, Nadia & Damak, Mondher & Yaakoubi, Nejib, 2022. "Dirichlet eigenvalue problems of irreversible Langevin diffusion," Statistics & Probability Letters, Elsevier, vol. 180(C).
    2. Franke, B. & Hwang, C.-R. & Ouled Said, A. & Pai, H.-M., 2021. "A note on the asymptotic variance of drift accelerated diffusions," Statistics & Probability Letters, Elsevier, vol. 175(C).
    3. Marie Vialaret & Florian Maire, 2020. "On the Convergence Time of Some Non-Reversible Markov Chain Monte Carlo Methods," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1349-1387, September.
    4. Ouled Said, A., 2020. "Some remark on the asymptotic variance in a drift accelerated diffusion," Statistics & Probability Letters, Elsevier, vol. 162(C).

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