## Coherent inference after checking a prior

D. R. Bickel, “Bayesian revision of a prior given prior-data conflict, expert opinion, or a similar insight: A large-deviation approach,” Working Paper, University of Ottawa, deposited in uO Research at http://hdl.handle.net/10393/34089/ (2015). 2015 preprint

## How to use priors with caution

D. R. Bickel, “Controlling the degree of caution in statistical inference with the Bayesian and frequentist approaches as opposite extremes,” *Electronic Journal of Statistics* **6**, 686-709 (2012). Full text (open access) | 2011 preprint

This paper reports a novel probability-interval framework for combining strengths of frequentist and Bayesian methods on the basis of game-theoretic first principles. It enables data analysis on the basis of the posterior distribution that is a blend between a set of plausible Bayesian posterior distributions and a parameter distribution that represents an alternative method of data analysis. This paper’s framework of statistical inference is intended to facilitate the development of new methods to bridge the gap between the frequentist and Bayesian approaches. Four concrete examples illustrate how such intermediate methods can leverage strengths of the two extreme approaches.