## Erratum: “Simple estimators of false discovery rates given as few as one or two p-values without strong parametric assumptions”

**Main entry:** Small dimensional empirical Bayes inference

## Coherent fiducial distributions

D. R. Bickel and M. Padilla, “A prior-free framework of coherent inference and its derivation of simple shrinkage estimators,” *Journal of Statistical Planning and Inference* **145**, 204–221 (2014). 2012 version

## Small dimensional empirical Bayes inference

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:

- proven asymptotic conservatism;
- simplicity of calculation without the tuning of smoothing parameters;
- no strong parametric assumptions;
- 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.

## Profile likelihood & MDL for measuring the strength of evidence

D. R. Bickel, “Pseudo-likelihood, explanatory power, and Bayes’s theorem [Comment on ‘A likelihood paradigm for clinical trials’],” *Journal of Statistical Theory and Practice* **7**, 178-182 (2013).

## Estimates of the local FDR

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

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.