Archive for the ‘fiducial inference’ Category

Evidential unification of confidence and empirical Bayes methods

1 March 2019 Leave a comment

Fiducial model averaging of Bayesian models and of frequentist models

1 January 2019 Leave a comment

D. R. Bickel, “A note on fiducial model averaging as an alternative to checking Bayesian and frequentist models,” Communications in Statistics – Theory and Methods 47, 3125-3137 (2018). Full article2015 preprint

“A Litany of Problems With p-values”

15 December 2018 Leave a comment

Bayesian, likelihoodist, and frequentist views appear in the comments in Statistical Thinking: A Litany of Problems With p-values.

Lower the statistical significance threshold to 0.005—or 0.001?

1 October 2018 Leave a comment

Pre-data insights update priors via Bayes’s theorem

1 September 2018 Leave a comment

How to adjust statistical inferences for the simplicity of distributions

1 August 2018 Leave a comment

Uncertainty propagation for empirical Bayes interval estimates: A fiducial approach

1 December 2017 Leave a comment

D. R. Bickel, “Confidence distributions applied to propagating uncertainty to inference based on estimating the local false discovery rate: A fiducial continuum from confidence sets to empirical Bayes set estimates as the number of comparisons increases,” Communications in Statistics – Theory and Methods 46, 10788-10799 (2017). Published article | Free access (limited time)2014 preprint

Publication Cover

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.