Archive
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.
MLE of the local FDR
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
Confidence levels as degrees of belief
D. R. Bickel, “A frequentist framework of inductive reasoning,” Sankhya A 74, 141-169 (2013). published version | 2009 version 
| relationship to a working paper | simple explanation (added 17 July 2017)
A confidence measure is a parameter distribution that encodes all confidence intervals for a given data set, model, and pivot. This article establishes some properties of the confidence measure that commend it as a viable alternative to the Bayesian posterior distribution.
Confidence (correct frequentist coverage) and coherence (compliance with Ramsey-type restrictions on rational belief) are both presented as desirable properties. The only distributions on a scalar parameter space that have both properties are confidence measures.
Local FDR estimation for low-dimensional data
M. Padilla and D. R. Bickel, “Estimators of the local false discovery rate designed for small numbers of tests,” Statistical Applications in Genetics and Molecular Biology 11 (5), art. 4 (2012). Full article | 2010 & 2012 preprints
How to combine statistical methods
D. R. Bickel, “Game-theoretic probability combination with applications to resolving conflicts between statistical methods,” International Journal of Approximate Reasoning 53, 880-891 (2012). Full article | 2011 preprint | Slides | Simple explanation
This paper proposes both a novel solution to the problem of combining probability distributions and a framework for using the new method to combine the results of differing statistical methods that may legitimately be used to analyze the same data set. While the paper emphasizes theoretical development, it is motivated by the need to combine two conflicting estimators of the probability of differential gene expression.
Extending the likelihood paradigm
D. R. Bickel, “The strength of statistical evidence for composite hypotheses: Inference to the best explanation,” Statistica Sinica 22, 1147-1198 (2012). Full article | 2010 version
