Revisiting Identification Concepts in Bayesian Analysis

Jean-Pierre Florens and Anna Simoni
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Jean-Pierre Florens: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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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.

Keywords: Minimal Sufficiency; Exact Estimability; Set identification; Dirichlet Process; Capacity functional; Nonparametric models. (search for similar items in EconPapers)
Date: 2021
New Economics Papers: this item is included in nep-dcm and nep-his
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Published in Annals of Economics and Statistics, 2021, 144, pp.1-38. ⟨10.15609/annaeconstat2009.144.0001⟩

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Journal Article: Revisiting Identification Concepts in Bayesian Analysis (2021)
Working Paper: Revisiting identification concepts in Bayesian analysis (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03504692

DOI: 10.15609/annaeconstat2009.144.0001

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