Archive for the ‘Types of data’ Category

Maximum entropy over a set of posteriors

10 August 2015 Leave a comment

D. R. Bickel, “Blending Bayesian and frequentist methods according to the precision of prior information with applications to hypothesis testing,” Statistical Methods & Applications 24, 523-546 (2015). Published article2012 preprint | 2011 preprint | Slides | Simple explanation


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 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.

Small-scale empirical Bayes & fiducial estimators

22 March 2015 Leave a comment

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 (2015). 2015 preprint

Self-consistent frequentism without fiducialism

3 September 2014 Leave a comment

Small dimensional empirical Bayes inference

9 May 2013 Leave a comment

D. R. Bickel, “Simple estimators of false discovery rates given as few as one or two p-values without strong parametric assumptions,” Statistical Applications in Genetics and Molecular Biology 12, 529–543 (2013). 2011 version | erratum


To address multiple comparison problems in small-to-high-dimensional biology, this paper introduces estimators of the local false discovery rate (LFDR), reports their main properties, and illustrates their use with proteomics data. The new estimators have the following advantages:

  1. proven asymptotic conservatism;
  2. simplicity of calculation without the tuning of smoothing parameters;
  3. no strong parametric assumptions;
  4. applicability to very small numbers of hypotheses as well as to very large numbers of hypotheses.

The link to the erratum was added 31 March 2015.

Estimates of the local FDR

13 February 2013 Leave a comment

Z. Yang, Z. Li, and D. R. Bickel, “Empirical Bayes estimation of posterior probabilities of enrichment: A comparative study of five estimators of the local false discovery rate,” BMC Bioinformatics 14, art. 87 (2013). published version |  2011 version | 2010 version


This paper adapts novel empirical Bayes methods for the problem of detecting enrichment in the form of differential representation of genes associated with a biological category with respect to a list of genes identified as differentially expressed. Read more…

Optimal strength of evidence

13 February 2013 Leave a comment

D. R. Bickel, “Minimax-optimal strength of statistical evidence for a composite alternative hypothesis,” International Statistical Review 81, 188-206 (2013). 2011 version | Simple explanation (added 2 July 2017)


This publication generalizes the likelihood measure of evidential support for a hypothesis with the help of tools originally developed by information theorists for minimizing the number of letters in a message. The approach is illustrated with an application to proteomics data.

MLE of the local FDR

13 February 2013 Comments off

Y. Yang, F. A. Aghababazadeh, and D. R. Bickel, “Parametric estimation of the local false discovery rate for identifying genetic associations,” IEEE/ACM Transactions on Computational Biology and Bioinformatics 10, 98-108 (2013). 2010 version | Slides


Read more…