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Efficiency and Convergence Properties of Slice Samplers

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  • ANTONIETTA MIRA
  • LUKE TIERNEY

Abstract

The slice sampler (SS) is a method of constructing a reversible Markov chain with a specified invariant distribution. Given an independence Metropolis–Hastings algorithm (IMHA) it is always possible to construct a SS that dominates it in the Peskun sense. This means that the resulting SS produces estimates with a smaller asymptotic variance than the IMHA. Furthermore the SS has a smaller second‐largest eigenvalue. This ensures faster convergence to the target distribution. A sufficient condition for uniform ergodicity of the SS is given and an upper bound for the rate of convergence to stationarity is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:29:y:2002:i:1:p:1-12
    DOI: 10.1111/1467-9469.00267
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    Cited by:

    1. Zhongxian Men & Tony S. Wirjanto & Adam W. Kolkiewicz, 2021. "Multiscale Stochastic Volatility Model with Heavy Tails and Leverage Effects," JRFM, MDPI, vol. 14(5), pages 1-28, May.
    2. Li, Yanxin & Walker, Stephen G., 2023. "A latent slice sampling algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    3. Minjung Kyung & Jeff Gill & George Casella, 2011. "Sampling schemes for generalized linear Dirichlet process random effects models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(3), pages 259-290, August.
    4. Luciano Fratocchi & Alberto Onetti & Alessia Pisoni, 2007. "Subsidiary’s Embeddedness of Italian SMEs in Central and Eastern European Countries (CEECs)," Economics and Quantitative Methods qf0703, Department of Economics, University of Insubria.
    5. Antonietta Mira & Daniel J. Sargent, 2003. "A new strategy for speeding Markov chain Monte Carlo algorithms," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 12(1), pages 49-60, February.
    6. Chib, Siddhartha, 2004. "Markov Chain Monte Carlo Technology," Papers 2004,22, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    7. Meyer, Renate & Cai, Bo & Perron, François, 2008. "Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3408-3423, March.
    8. Ghosal, Rahul & Ghosh, Sujit K., 2022. "Bayesian inference for generalized linear model with linear inequality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 166(C).
    9. Zhongxian Men & Adam W. Kolkiewicz & Tony S. Wirjanto, 2019. "Threshold Stochastic Conditional Duration Model for Financial Transaction Data," JRFM, MDPI, vol. 12(2), pages 1-21, May.
    10. 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.
    11. Federico Bassetti & Fabrizio Leisen, 2007. "Metropolis Algorithm and equienergy sampling for two mean field spin systems," Economics and Quantitative Methods qf0704, Department of Economics, University of Insubria.
    12. Anagh Chattopadhyay & Soudeep Deb, 2024. "A spatio-temporal model for binary data and its application in analyzing the direction of COVID-19 spread," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(4), pages 823-851, December.
    13. Gareth W. Peters & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "Dynamic operational risk: modeling dependence and combining different sources of information," Papers 0904.4074, arXiv.org, revised Jul 2009.

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