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Methods for computing marginal data densities from the Gibbs output

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  • Fuentes-Albero, Cristina
  • Melosi, Leonardo

Abstract

We introduce two estimators for estimating the Marginal Data Density (MDD) from the Gibbs output. Our methods are based on exploiting the analytical tractability condition, which requires that some parameter blocks can be analytically integrated out from the conditional posterior densities. This condition is satisfied by several widely used time series models. An empirical application to six-variate VAR models shows that the bias of a fully computational estimator is sufficiently large to distort the implied model rankings. One of the estimators is fast enough to make multiple computations of MDDs in densely parameterized models feasible.

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  • Fuentes-Albero, Cristina & Melosi, Leonardo, 2013. "Methods for computing marginal data densities from the Gibbs output," Journal of Econometrics, Elsevier, vol. 175(2), pages 132-141.
  • Handle: RePEc:eee:econom:v:175:y:2013:i:2:p:132-141
    DOI: 10.1016/j.jeconom.2013.03.002
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    7. Benjamin K. Johannsen & Elmar Mertens, 2021. "A Time‐Series Model of Interest Rates with the Effective Lower Bound," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 53(5), pages 1005-1046, August.
    8. Sebastian Ankargren & Måns Unosson & Yukai Yang, 2018. "A mixed-frequency Bayesian vector autoregression with a steady-state prior," CREATES Research Papers 2018-32, Department of Economics and Business Economics, Aarhus University.
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    More about this item

    Keywords

    Marginal likelihood; Gibbs sampler; Time series econometrics; Bayesian econometrics; Reciprocal importance sampling;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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