A note on fiducial model averaging as an alternative to checking Bayesian and frequentist models |
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Authors: | David R. Bickel |
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Affiliation: | 1. Ottawa Institute of Systems Biology, Department of Biochemistry, Microbiology and Immunology, Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canadadbickel@uottawa.ca |
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Abstract: | Just as frequentist hypothesis tests have been developed to check model assumptions, prior predictive p-values and other Bayesian p-values check prior distributions as well as other model assumptions. These model checks not only suffer from the usual threshold dependence of p-values, but also from the suppression of model uncertainty in subsequent inference. One solution is to transform Bayesian and frequentist p-values for model assessment into a fiducial distribution across the models. Averaging the Bayesian or frequentist posterior distributions with respect to the fiducial distribution can reproduce results from Bayesian model averaging or classical fiducial inference. |
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Keywords: | Bayesian model averaging coherent fiducial distribution confidence distribution distributional inference fiducial inference frequentist model averaging model assessment model checking model criticism posterior predictive check prior predictive check prior-data conflict. |
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