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Revisiting Identification Concepts in Bayesian Analysis

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  • Jean-Pierre Florens
  • Anna Simoni

Abstract

This paper studies the role played by identification in the Bayesian analysis of statistical and econometric models. First, for unidentified models we demonstrate that there are situations where the introduction of a non-degenerate prior distribution can make a parameter that is nonidentified in frequentist theory identified in Bayesian theory. In other situations, it is preferable to work with the unidentified model and construct a Markov Chain Monte Carlo (MCMC) algorithms for it instead of introducing identifying assumptions. Second, for partially identified models we demonstrate how to construct the prior and posterior distributions for the identified set parameter and how to conduct Bayesian analysis. Finally, for models that contain some parameters that are identified and others that are not we show that marginalizing out the identified parameter from the likelihood with respect to its conditional prior, given the nonidentified parameter, allows the data to be informative about the nonidentified and partially identified parameter. The paper provides examples and simulations that illustrate how to implement our techniques.

Suggested Citation

  • Jean-Pierre Florens & Anna Simoni, 2021. "Revisiting Identification Concepts in Bayesian Analysis," Annals of Economics and Statistics, GENES, issue 144, pages 1-38.
  • Handle: RePEc:adr:anecst:y:2021:i:144:p:1-38
    DOI: https://doi.org/10.15609/annaeconstat2009.144.0001
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    More about this item

    Keywords

    Minimal Sufficiency; Exact Estimability; Set identification; Dirichlet Process; Capacity Functional; Nonparametric Models;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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