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December 2004 A Bayesian χ2 test for goodness-of-fit
Valen E. Johnson
Ann. Statist. 32(6): 2361-2384 (December 2004). DOI: 10.1214/009053604000000616


This article describes an extension of classical χ2 goodness-of-fit tests to Bayesian model assessment. The extension, which essentially involves evaluating Pearson’s goodness-of-fit statistic at a parameter value drawn from its posterior distribution, has the important property that it is asymptotically distributed as a χ2 random variable on K−1 degrees of freedom, independently of the dimension of the underlying parameter vector. By examining the posterior distribution of this statistic, global goodness-of-fit diagnostics are obtained. Advantages of these diagnostics include ease of interpretation, computational convenience and favorable power properties. The proposed diagnostics can be used to assess the adequacy of a broad class of Bayesian models, essentially requiring only a finite-dimensional parameter vector and conditionally independent observations.


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Valen E. Johnson. "A Bayesian χ2 test for goodness-of-fit." Ann. Statist. 32 (6) 2361 - 2384, December 2004.


Published: December 2004
First available in Project Euclid: 7 February 2005

zbMATH: 1068.62028
MathSciNet: MR2153988
Digital Object Identifier: 10.1214/009053604000000616

Primary: 62C10
Secondary: 62E20

Keywords: Bayes factor , Bayesian model assessment , discrepancy functions , intrinsic Bayes factor , Pearson’s chi-squared statistic , posterior-predictive diagnostics, p-value

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 6 • December 2004
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