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The slice sampler and centrally symmetric distributions

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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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    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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