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Properties of nested sampling

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  • Nicolas Chopin
  • Christian P. Robert

Abstract

Nested sampling is a simulation method for approximating marginal likelihoods. We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is asymptotically Gaussian. It is shown that the asymptotic variance of the nested sampling approximation typically grows linearly with the dimension of the parameter. We discuss the applicability and efficiency of nested sampling in realistic problems, and compare it with two current methods for computing marginal likelihood. Finally, we propose an extension that avoids resorting to Markov chain Monte Carlo simulation to obtain the simulated points. Copyright 2010, Oxford University Press.

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  • Nicolas Chopin & Christian P. Robert, 2010. "Properties of nested sampling," Biometrika, Biometrika Trust, vol. 97(3), pages 741-755.
    • Handle: RePEc:oup:biomet:v:97:y:2010:i:3:p:741-755
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    File URL: http://hdl.handle.net/10.1093/biomet/asq021
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    References listed on IDEAS

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    1. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
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    5. Sylvia Fruhwirth-Schnatter, 2004. "Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 143-167, June.
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    1. Gelman Andrew & Robert Christian P. & Rousseau Judith, 2013. "Inherent difficulties of non-Bayesian likelihood-based inference, as revealed by an examination of a recent book by Aitkin," Statistics & Risk Modeling, De Gruyter, vol. 30(2), pages 105-120, June.
    2. Tahir Ekin & Nicholas G. Polson & Refik Soyer, 2017. "Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(8), pages 613-627, December.
    3. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    4. Christian P. Robert & Gareth Roberts, 2021. "Rao–Blackwellisation in the Markov Chain Monte Carlo Era," International Statistical Review, International Statistical Institute, vol. 89(2), pages 237-249, August.
    5. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    6. Christian P. Robert, 2013. "Bayesian Computational Tools," Working Papers 2013-45, Center for Research in Economics and Statistics.
    7. Nicolas Chopin & Alessandra Iacobucci & Jean-Michel Marin & Kerrie L. Mengersen & Christian P. Robert & Robin Ryder & Christian Schafer, 2010. "On Particle Learning," Working Papers 2010-22, Center for Research in Economics and Statistics.

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