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Efficient importance sampling in low dimensions using affine arithmetic

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  • Richard G. Everitt

    (Whiteknights)

Abstract

Despite the development of sophisticated techniques such as sequential Monte Carlo (Del Moral et al. in J R Stat Soc Ser B 68(3):411–436, 2006), importance sampling (IS) remains an important Monte Carlo method for low dimensional target distributions (Chopin and Ridgway in Leave Pima Indians alone: binary regression as a benchmark for Bayesian computation, 32:64–87, 2017). This paper describes a new technique for constructing proposal distributions for IS, using affine arithmetic (de Figueiredo and Stolfi in Numer Algorithms 37(1–4):147–158, 2004). This work builds on the Moore rejection sampler (Sainudiin in Machine interval experiments, Cornell University, Ithaca, 2005; Sainudiin and York in Algorithms Mol Biol 4(1):1, 2009) to which we provide a comparison.

Suggested Citation

  • Richard G. Everitt, 2018. "Efficient importance sampling in low dimensions using affine arithmetic," Computational Statistics, Springer, vol. 33(1), pages 1-29, March.
  • Handle: RePEc:spr:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0729-z
    DOI: 10.1007/s00180-017-0729-z
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    References listed on IDEAS

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    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    3. Luca Martino & Jesse Read, 2013. "On the flexibility of the design of multiple try Metropolis schemes," Computational Statistics, Springer, vol. 28(6), pages 2797-2823, December.
    4. W. R. Gilks & N. G. Best & K. K. C. Tan, 1995. "Adaptive Rejection Metropolis Sampling Within Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 455-472, December.
    5. Maxime Lenormand & Franck Jabot & Guillaume Deffuant, 2013. "Adaptive approximate Bayesian computation for complex models," Computational Statistics, Springer, vol. 28(6), pages 2777-2796, December.
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