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

By Valen E. Johnson. 2004

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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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8499b9df2561d1204b73df6d5c6e01761fb5442e

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In Statistics and Probability

Citations in the corpus

Bayesian Model Assessment Using Pivotal Quantities (2007, methodology): “This difficulty was discussed in Johnson (2004) for the special case of pivotal statistics based on Pearson’s chi-squared goodness-of-fit test.”