## Empirical Bayes single-comparison procedure

D. R. Bickel, “Small-scale inference: Empirical Bayes and confidence methods for as few as a single comparison,” *International Statistical Review ***82**, 457-476 (2014). Published version | 2011 preprint | Simple explanation (link added 21 June 2017)

Parametric empirical Bayes methods of estimating the local false discovery rate by maximum likelihood apply not only to the large-scale settings for which they were developed, but, with a simple modification, also to small numbers of comparisons. In fact, data for a single comparison are sufficient under broad conditions, as seen from applications to measurements of the abundance levels of 20 proteins and from simulation studies with confidence-based inference as the competitor.

## 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).