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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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File URL: http://hdl.handle.net/10.1093/biomet/asq021
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Bibliographic Info

Article provided by Biometrika Trust in its journal Biometrika.

Volume (Year): 97 (2010)
Issue (Month): 3 ()
Pages: 741-755

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Handle: RePEc:oup:biomet:v:97:y:2010:i:3:p:741-755

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  1. 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.
  2. 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, 06.
  3. Francesco Bartolucci & Luisa Scaccia & Antonietta Mira, 2006. "Efficient Bayes factor estimation from the reversible jump output," Biometrika, Biometrika Trust, vol. 93(1), pages 41-52, March.
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Cited by:
  1. Christian P. Robert, 2013. "Bayesian Computational Tools," Working Papers 2013-45, Centre de Recherche en Economie et Statistique.

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