## Adaptively selecting an empirical Bayes reference class

F. A. Aghababazadeh, M. Alvo, and D. R. Bickel, “Estimating the local false discovery rate via a bootstrap solution to the reference class problem,” Working Paper, University of Ottawa, deposited in uO Research at http://hdl.handle.net/10393/34295 (2016). 2016 preprint

## 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

## Fiducial model averages from model checks

D. R. Bickel, “A note on fiducial model averaging as an alternative to checking Bayesian and frequentist models,” Working Paper, University of Ottawa, deposited in uO Research at http://hdl.handle.net/10393/32313 (2015). 2015 preprint

## Small-scale empirical Bayes & fiducial estimators

M. Padilla and D. R. Bickel, “Empirical Bayes and fiducial effect-size estimation for small numbers of tests,” Working Paper, University of Ottawa, deposited in uO Research at http://hdl.handle.net/10393/32151 (2015). 2015 preprint

## Model fusion & multiple testing in the likelihood paradigm

D. R. Bickel, “Model fusion and multiple testing in the likelihood paradigm: Shrinkage and evidence supporting a point null hypothesis,” Working Paper, University of Ottawa, deposited in uO Research at http://hdl.handle.net/10393/31897 (2014). 2014 preprint | Supplement (link added 10 February 2015)

Errata for Theorem 4:

- The weights of evidence should not be conditional.
- Some of the equal signs should be “is a member of” signs.

## Fiducial error propagation for empirical Bayes set estimates

D. R. Bickel, “A fiducial continuum from confidence sets to empirical Bayes set estimates as the number of comparisons increases,” Working Paper, University of Ottawa, deposited in uO Research at http://hdl.handle.net/10393/31898 (2014). 2014 preprint

Two problems confronting the eclectic approach to statistics result from its lack of a unifying theoretical foundation. First, there is typically no continuity between a p-value reported as a level of evidence for a hypothesis in the absence of the information needed to estimate a relevant prior on one hand and an estimated posterior probability of a hypothesis reported in the presence of such information on the other hand. Second, the empirical Bayes methods recommended do not propagate the uncertainty due to estimating the prior.

The latter problem is addressed by applying a coherent form of fiducial inference to hierarchical models, yielding empirical Bayes set estimates that reflect uncertainty in estimating the prior. Plugging in the maximum likelihood estimator, while not propagating that uncertainty, provides continuity from single comparisons to large numbers of comparisons.