Analysis of variance for bayesian inference
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
|Date of creation:||Dec 2011|
|Date of revision:|
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- Frank Smets & Raf Wouters, 2007.
"Shocks and Frictions in US Business Cycles : a Bayesian DSGE Approach,"
Working Paper Research
109, National Bank of Belgium.
- 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.
- Smets, Frank & Wouters, Raf, 2007. "Shocks and frictions in US business cycles: a Bayesian DSGE approach," Working Paper Series 0722, European Central Bank.
- Smets, Frank & Wouters, Rafael, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," CEPR Discussion Papers 6112, C.E.P.R. Discussion Papers.
- L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters, in: Credit and State Theories of Money, chapter 1 Edward Elgar Publishing.
- Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
- Arnold Zellner, 1997. "Bayesian Analysis in Econometrics and Statistics," Books, Edward Elgar Publishing, number 825.
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