Analysis of Variance for Bayesian Inference

24 Pages Posted: 21 Dec 2011

See all articles by John Geweke

John Geweke

University of Technology Sydney - Economics Discipline Group

Gianni Amisano

Board of Governors of the Federal Reserve System; European Central Bank (ECB); University of Bologna - Rimini Center for Economic Analysis (RCEA); University of Brescia - Department of Economics

Date Written: December 7, 2011

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.

Keywords: Analysis of variance, Bayesian inference, predictive distributions

JEL Classification: C11, C53

Suggested Citation

Geweke, John and Amisano, Gianni, Analysis of Variance for Bayesian Inference (December 7, 2011). ECB Working Paper No. 1409, Available at SSRN: https://ssrn.com/abstract=1969437 or http://dx.doi.org/10.2139/ssrn.1969437

John Geweke (Contact Author)

University of Technology Sydney - Economics Discipline Group ( email )

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HOME PAGE: http://www.censoc.uts.edu.au/about/members/jgeweke_papers.html

Gianni Amisano

Board of Governors of the Federal Reserve System

20th Street and Constitution Avenue NW
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United States

European Central Bank (ECB) ( email )

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University of Bologna - Rimini Center for Economic Analysis (RCEA) ( email )

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Italy

University of Brescia - Department of Economics ( email )

Via San Faustino 74B
Brescia, 25122
Italy

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