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

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dc.creatorJohnson, Valen E.
dc.date2005-08-30
dc.date.accessioned2026-07-07T08:07:14Z
dc.date.available2026-07-07T08:07:14Z
dc.descriptionThis article describes an extension of classical χ^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 χ^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.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053604000000616 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0508593
dc.identifierhttp://arxiv.org/abs/math/0508593
dc.identifierAnnals of Statistics 2004, Vol. 32, No. 6, 2361-2384
dc.identifierdoi:10.1214/009053604000000616
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130874
dc.subjectStatistics Theory
dc.subject62C10 (Primary) 62E20. (Secondary)
dc.titleA Bayesian χ^2 test for goodness-of-fit
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