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A Bayesian Chi-Squared Test for Goodness of Fit

Author

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  • Valen Johnson

    (University of Michigan School of Public Health)

Abstract
This article describes an extension of classical x 2 goodness-of-fit tests to Bayesian model assessment. The extension, which essentially involvesevaluating Pearson's goodness-of-fit statistic at a parameter value drawn from its posterior distribution, has the important property that it is asymptoti-cally distributed as a x2 random variable on K-1 degrees of freedom, indepen-dently of the dimension of the underlying parameter vector. By averaging over the posterior distribution of this statistic, a global goodness-of-fit diagnostic is obtained. Advantages of this diagnostic{which may be interpreted as the area under an ROC curve{include ease of interpretation, computational conve-nience, and favorable power properties. The proposed diagnostic can be used to assess the adequacy of a broad class of Bayesian models, essentially requir- ing only a finite-dimensional parameter vector and conditionally independent observations.

Suggested Citation

  • Valen Johnson, 2004. "A Bayesian Chi-Squared Test for Goodness of Fit," The University of Michigan Department of Biostatistics Working Paper Series 1000, Berkeley Electronic Press.
    • Handle: RePEc:bep:mchbio:1000
    Note: oai:bepress.com:umichbiostat-1000
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    File URL: http://www.bepress.com/cgi/viewcontent.cgi?article=1000&context=umichbiostat
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    References listed on IDEAS

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    1. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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    Cited by:

    1. Timothy D. Johnson, 2007. "Analysis of Pulsatile Hormone Concentration Profiles with Nonconstant Basal Concentration: A Bayesian Approach," Biometrics, The International Biometric Society, vol. 63(4), pages 1207-1217, December.
    2. Bo Cai & David B. Dunson & Joseph B. Stanford, 2010. "Dynamic Model for Multivariate Markers of Fecundability," Biometrics, The International Biometric Society, vol. 66(3), pages 905-913, September.
    3. Peng, Weiwen & Li, Yan-Feng & Yang, Yuan-Jian & Huang, Hong-Zhong & Zuo, Ming J., 2014. "Inverse Gaussian process models for degradation analysis: A Bayesian perspective," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 175-189.
    4. Jing Cao & Ann Moosman & Valen E. Johnson, 2010. "A Bayesian Chi-Squared Goodness-of-Fit Test for Censored Data Models," Biometrics, The International Biometric Society, vol. 66(2), pages 426-434, June.

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