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The slice sampler and centrally symmetric distributions

Author

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  • Planas Christophe

    (European Commission, Joint Research Centre, Ispra, Italy)

  • Rossi Alessandro

    (European Commission, Joint Research Centre, Ispra, Italy)

Abstract

We show that the slice sampler generates Markov chains whose variables are mean independent and thus uncorrelated when the target density is centrally symmetric. Skewness instead boosts correlations. Popular implementation algorithms such as stepping-out and multivariate-sampling-with-hyperrectangles add statistical inefficiency, the first in case of multimodality, the second in all circumstances. A new sampler which exploits these structural and algorithmic characteristics to reduce the variance of Monte Carlo estimates is experimented in several sampling problems. An insight into the properties of the product slice sampler is also provided.

Suggested Citation

  • Planas Christophe & Rossi Alessandro, 2024. "The slice sampler and centrally symmetric distributions," Monte Carlo Methods and Applications, De Gruyter, vol. 30(3), pages 299-313.
    • Handle: RePEc:bpj:mcmeap:v:30:y:2024:i:3:p:299-313:n:1007
    DOI: 10.1515/mcma-2024-2012
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    1. P. Damlen & J. Wakefield & S. Walker, 1999. "Gibbs sampling for Bayesian non‐conjugate and hierarchical models by using auxiliary variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 331-344, April.
    2. Harman, Radoslav & Lacko, Vladimír, 2010. "On decompositional algorithms for uniform sampling from n-spheres and n-balls," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2297-2304, November.
    3. Brendan Kline & Elie Tamer, 2016. "Bayesian inference in a class of partially identified models," Quantitative Economics, Econometric Society, vol. 7(2), pages 329-366, July.
    4. Li, Junye, 2011. "Volatility components, leverage effects, and the return-volatility relations," Journal of Banking & Finance, Elsevier, vol. 35(6), pages 1530-1540, June.
    5. Dunson, David B. & Xing, Chuanhua, 2009. "Nonparametric Bayes Modeling of Multivariate Categorical Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1042-1051.
    6. Leemis, Lawrence M. & McQueston, Jacquelyn T., 2008. "Univariate Distribution Relationships," The American Statistician, American Statistical Association, vol. 62, pages 45-53, February.
    7. Gareth O. Roberts & Jeffrey S. Rosenthal, 1999. "Convergence of Slice Sampler Markov Chains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 643-660.
    8. George S. Fishman, 1999. "An Analysis of Swendsen–Wang and Related Sampling Methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 623-641.
    9. Berger J.O. & De Oliveira V. & Sanso B., 2001. "Objective Bayesian Analysis of Spatially Correlated Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1361-1374, December.
    10. Sudipto Banerjee, 2005. "On Geodetic Distance Computations in Spatial Modeling," Biometrics, The International Biometric Society, vol. 61(2), pages 617-625, June.
    11. Antonietta Mira & Luke Tierney, 2002. "Efficiency and Convergence Properties of Slice Samplers," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 1-12, March.
    12. Yang, Zhenlin, 2006. "A modified family of power transformations," Economics Letters, Elsevier, vol. 92(1), pages 14-19, July.
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    More about this item

    Keywords

    Markov chain Monte Carlo; multivariate sampling; inefficiency factor;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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