Doklady Mathematics

, Volume 93, Issue 2, pp 155–158 | Cite as

Nonasymptotic approach to Bayesian semiparametric inference

Mathematics
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Abstract

The classical semiparametric Bernstein–von Mises (BvM) results is reconsidered in a non-classical setup allowing finite samples and model misspecication. We obtain an upper bound on the error of Gaussian approximation of the posterior distribution for the target parameter which is explicit in the dimension of the target parameter and in the dimension of sieve approximation of the nuisance parameter. This helps to identify the so called critical dimension p n of the sieve approximation of the full parameter for which the BvM result is applicable. If the bias induced by sieve approximation is small and dimension of sieve approximation is smaller then critical dimension than the BvM result is valid. In the important i.i.d. and regression cases, we show that the condition “p n 2 q/n is small”, where q is the dimension of the target parameter and n is the sample size, leads to the BvM result under general assumptions on the model.

Keywords

Nuisance Parameter Fisher Information Matrix Target Parameter Gaussian Process Regression Full Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyi, Moscow oblastRussia
  3. 3.Datadvance CompanyMoscowRussia

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