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Analysis of variance for bayesian inference

Author

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  • Amisano, Gianni
  • Geweke, John

Abstract

This paper develops a multi-way analysis of variance for non-Gaussian multivariate distributions and provides a practical simulation algorithm to estimate the corresponding components of variance. It specifically addresses variance in Bayesian predictive distributions, showing that it may be decomposed into the sum of extrinsic variance, arising from posterior uncertainty about parameters, and intrinsic variance, which would exist even if parameters were known. Depending on the application at hand, further decomposition of extrinsic or intrinsic variance (or both) may be useful. The paper shows how to produce simulation-consistent estimates of all of these components, and the method demands little additional effort or computing time beyond that already invested in the posterior simulator. It illustrates the methods using a dynamic stochastic general equilibrium model of the US economy, both before and during the global financial crisis. JEL Classification: C11, C53

Suggested Citation

  • Amisano, Gianni & Geweke, John, 2011. "Analysis of variance for bayesian inference," Working Paper Series 1409, European Central Bank.
  • Handle: RePEc:ecb:ecbwps:20111409
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    File URL: https://www.ecb.europa.eu//pub/pdf/scpwps/ecbwp1409.pdf
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    References listed on IDEAS

    as
    1. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    2. L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters,in: Credit and State Theories of Money, chapter 1 Edward Elgar Publishing.
    3. John Geweke, 2010. "Complete and Incomplete Econometric Models," Economics Books, Princeton University Press, edition 1, number 9218.
    4. Arnold Zellner, 1997. "Bayesian Analysis in Econometrics and Statistics," Books, Edward Elgar Publishing, number 825, April.
    5. Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
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    1. repec:wly:japmet:v:32:y:2017:i:1:p:103-119 is not listed on IDEAS
    2. repec:oup:jfinec:v:16:y:2018:i:1:p:34-62. is not listed on IDEAS
    3. Anders Warne & Günter Coenen & Kai Christoffel, 2017. "Marginalized Predictive Likelihood Comparisons of Linear Gaussian State‐Space Models with Applications to DSGE, DSGE‐VAR, and VAR Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 103-119, January.
    4. Daniele Bianchi & Massimo Guidolin & Francesco Ravazzolo, 2013. "Dissecting the 2007-2009 real estate market bust: systematic pricing correction or just a housing fad?," Working Paper 2013/22, Norges Bank.
    5. Kajal Lahiri & Huaming Peng & Xuguang Sheng, 2015. "Measuring Uncertainty of a Combined Forecast and Some Tests for Forecaster Heterogeneity," CESifo Working Paper Series 5468, CESifo Group Munich.
    6. Kolasa, Marcin & Rubaszek, Michał, 2015. "Forecasting using DSGE models with financial frictions," International Journal of Forecasting, Elsevier, vol. 31(1), pages 1-19.

    More about this item

    Keywords

    analysis of variance; Bayesian inference; posterior simulation; predictive distributions;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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