A Bayesian χ^2 test for goodness-of-fit

Details A Bayesian χ^2 test for goodness-of-fit A Bayesian χ^2 test for goodness-of-fit

2005-08-30

arxiv.org/abs/math/0508593v1

Annals of Statistics 2004, Vol. 32, No. 6, 2361-2384

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000616 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000000616

This article describes an extension of classical \chi^2 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 \chi^2 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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