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Quantitative approximations of evolving probability measures and sequential Markov chain Monte Carlo methods
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  • Published: 17 January 2012

Quantitative approximations of evolving probability measures and sequential Markov chain Monte Carlo methods

  • Andreas Eberle1 &
  • Carlo Marinelli1,2 

Probability Theory and Related Fields volume 155, pages 665–701 (2013)Cite this article

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  • 3 Citations

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Abstract

We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity conditions, we derive non-asymptotic error bounds for the particle system approximation. In a few simple examples, including high dimensional product measures, bounds with explicit constants of feasible size are obtained. Our main motivation are applications to sequential MCMC methods for Monte Carlo integral estimation.

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Andreas Eberle & Carlo Marinelli

  2. Facoltà di Economia, Università di Bolzano, Piazza Università 1, 39100, Bolzano, Italy

    Carlo Marinelli

Authors
  1. Andreas Eberle
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  2. Carlo Marinelli
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Corresponding author

Correspondence to Andreas Eberle.

Additional information

We would like to thank the anonymous referees for detailed reports and very helpful comments on the first version of this article. This work was partially supported by the Sonderforschungsbereich 611, Bonn. The second-named author also gratefully acknowledges the support of the DAAD.

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Eberle, A., Marinelli, C. Quantitative approximations of evolving probability measures and sequential Markov chain Monte Carlo methods. Probab. Theory Relat. Fields 155, 665–701 (2013). https://doi.org/10.1007/s00440-012-0410-y

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  • Received: 12 November 2010

  • Revised: 16 July 2011

  • Published: 17 January 2012

  • Issue Date: April 2013

  • DOI: https://doi.org/10.1007/s00440-012-0410-y

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Keywords

  • Markov chain Monte Carlo
  • Sequential Monte Carlo
  • Importance sampling
  • Spectral gap
  • Dirichlet forms
  • Functional inequalities
  • Feynman–Kac formula

Mathematics Subject Classification (2000)

  • 65C05
  • 60J25
  • 60B10
  • 47H20
  • 47D08
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