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On the computational complexity of MCMC-based estimators in large samples

Author

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  • Alexandre Belloni

    (Institute for Fiscal Studies)

  • Victor Chernozhukov

    () (Institute for Fiscal Studies and MIT)

Abstract

In this paper we examine the implications of the statistical large sample theory for the computational complexity of Bayesian and quasi-Bayesian estimation carried out using Metropolis random walks. Our analysis is motivated by the Laplace-Bernstein-Von Mises central limit theorem, which states that in large samples the posterior or quasi-posterior approaches a normal density. Using this observation, we establish polynomial bounds on the computational complexity of general Metropolis random walks methods in large samples. Our analysis covers cases, where the underlying log-likelihood or extremum criterion function is possibly nonconcave, discontinuous, and of increasing dimension. However, the central limit theorem restricts the deviations from continuity and log-concavity of the log-likelihood or extremum criterion function in a very specific manner.

Suggested Citation

  • Alexandre Belloni & Victor Chernozhukov, 2007. "On the computational complexity of MCMC-based estimators in large samples," CeMMAP working papers CWP12/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:12/07
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    File URL: http://cemmap.ifs.org.uk/wps/cwp1207.pdf
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    References listed on IDEAS

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