Blending Bayesian and frequentist methods according to the precision of prior information with applications to hypothesis testing

  • David R. Bickel
  • Statistical Methods & Applications, February 2015, Springer Science + Business Media
  • DOI: 10.1007/s10260-015-0299-6

How to combine frequentist data analysis with Bayesian data analysis

What is it about?

In this general approach, Bayesian inference is used when the prior distribution is known, frequentist inference is used when nothing is known about the prior, and both types of inference are blended according to game theory when the prior is known to be a member of some set. (The robust Bayes framework represents knowledge about a prior in terms of a set of possible priors.) If the benchmark posterior that corresponds to frequentist inference lies within the set of Bayesian posteriors derived from the set of priors, then the benchmark posterior is used for inference. Otherwise, the posterior within that set that minimizes the cross entropy to the benchmark posterior is used for inference.

Why is it important?

This framework of statistical inference facilitates the development of new methodology to bridge the gap between the frequentist and Bayesian theories. As an example, a simple and practical method for combining p-values with a set of possible posterior probabilities is provided.


David R. Bickel
University of Ottawa

This paper relies on fiducial inference in the form of confidence distributions called confidence posteriors to emphasize their similarity to Bayesian posterior distributions. It illustrates a use of fiducial distributions that is in some ways more Bayesian than frequentist even though such distributions do not require the specification of a prior distribution.

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The following have contributed to this page: David R. Bickel