Archive
Maximum entropy over a set of posteriors
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 article | 2012 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.
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.
