Archive for the ‘preprints’ Category

False discovery rates are misleadingly low

2 March 2016 Leave a comment

Coherent inference after checking a prior

7 January 2016 Leave a comment

Fiducial model averages from model checks

10 May 2015 Leave a comment

Small-scale empirical Bayes & fiducial estimators

22 March 2015 Leave a comment

Model fusion & multiple testing in the likelihood paradigm

11 January 2015 Leave a comment

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 (2014). 2014 preprint | Supplement (link added 10 February 2015)

Errata for Theorem 4:

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

Fiducial error propagation for empirical Bayes set estimates

10 January 2015 Leave a comment

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 (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.

Self-consistent frequentism without fiducialism

3 September 2014 Leave a comment

Assessing multiple models

1 June 2014 Comments off

Bayes/non-Bayes blended inference

5 October 2012 Leave a comment

Updated with a new multiple comparison procedure and applications on 30 June 2012 and with slides for a presentation on 5 October 2012:

D. R. Bickel, “Blending Bayesian and frequentist methods according to the precision of prior information with applications to hypothesis testing,” Working Paper, University of Ottawa, deposited in uO Research at (2012)2012 preprint | 2011 preprint | Slides

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.

In this new approach to statistics, 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 is closest to the benchmark posterior is used for inference.

Confidence + coherence = fiducial shrinkage

30 June 2012 Leave a comment

D. R. Bickel, “A prior-free framework of coherent inference and its derivation of simple shrinkage estimators,” Working Paper, University of Ottawa, deposited in uO Research at (2012). 2012 preprint

This paper proposes a new method of shrinking point and interval estimates on the basis of fiducial inference. Since problems with the interpretation of fiducial probability have prevented its widespread use, this manuscript first places fiducial inference within a general framework that has Bayesian and frequentist foundations.