Bayesian Testing of a Parametric Model Versus Nonparametric Alternatives

James O. Berger and Alessandra Guglielmi

Testing the fit of data to a parametric model can be done by embedding the parametric model in a nonparametric alternative and computing the Bayes factor of the parametric model to the nonparametric alternative. Doing so by specifying the nonparametric alternative via a Polya tree process is particularly attractive, from both theoretical and methodological perspectives. Default (non-subjective) versions of this analysis are developed herein, and illustrated on various examples.

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