Averaging Bayesian or frequentist models via a confidence or fiducial distribution

What is it about?

The uncertainty in statistical model assumptions may be incorporated using developments of Fisher’s fiducial argument. The development used in this paper is the theory of coherent fiducial distributions, a generalization of the theory of confidence distributions. Averaging models with respect to confidence distributions or other fiducial distributions has advantages over Bayesian model averaging and frequentist model averaging.

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Why is it important?

In most applications of statistics to the analysis of data, there is uncertainty in the assumptions underlying the models. Such uncertainty is often accounted for using posterior predictive checks, Bayesian model averaging, or frequentist model averaging. Each approach has its own strengths and weaknesses. Some of the weaknesses are overcome by the proposed approach using coherent fiducial distributions of the models.

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