A Bayesian χ2 test for goodness-of-fit

The Annals of Statistics · 2004 · Volume 32 · Issue 6

Abstract

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.

Keywords

62C10, 62E20, Bayes factor, Bayesian model assessment, discrepancy functions, intrinsic Bayes factor, Pearson’s chi-squared statistic, posterior-predictive diagnostics, p-value

Enable JavaScript for citation tools and additional paper interactions.