#### 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.

#### Disciplines

Categorical Data Analysis | Clinical Epidemiology | Statistical Models

#### Suggested Citation

Johnson, Valen, "A Bayesian Chi-Squared Test for Goodness of Fit" (February 2004). *The University of Michigan Department of Biostatistics Working Paper Series.* Working Paper 1.

http://biostats.bepress.com/umichbiostat/paper1

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Categorical Data Analysis Commons, Clinical Epidemiology Commons, Statistical Models Commons