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Importance Sampling Via the Estimated Sampler

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  • Masayuki Henmi
  • Ryo Yoshida
  • Shinto Eguchi

Abstract

Monte Carlo importance sampling for evaluating numerical integration is discussed. We consider a parametric family of sampling distributions and propose the use of the sampling distribution estimated by maximum likelihood. The proposed method of importance sampling using the estimated sampling distribution is shown to improve the asymptotic variance of the ordinary method using the true sampling distribution. The argument is closely related to the discussion of the paradox in Henmi & Eguchi (2004). We focus on a condition under which the estimated integration value obtained by the proposed method has asymptotic zero variance. Copyright 2007, Oxford University Press.

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  • Masayuki Henmi & Ryo Yoshida & Shinto Eguchi, 2007. "Importance Sampling Via the Estimated Sampler," Biometrika, Biometrika Trust, vol. 94(4), pages 985-991.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:4:p:985-991
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    File URL: http://hdl.handle.net/10.1093/biomet/asm076
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    Cited by:

    1. Daniele Cuntrera & Vincenzo Falco & Ornella Giambalvo, 2022. "On the Sampling Size for Inverse Sampling," Stats, MDPI, vol. 5(4), pages 1-15, November.

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