Archive
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
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.
Estimating probabilities of enrichment
Z. Yang, Z. Li, and D. R. Bickel, “Empirical Bayes estimation of posterior probabilities of enrichment,” Technical Report, Ottawa Institute of Systems Biology, Technical Report, Ottawa Institute of Systems Biology, arXiv:1201.0153 (2011). Full preprint | 2010 seed
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. A microarray case study illustrates the methods using Gene Ontology (GO) terms, and a simulation study compares their performance. We report that which enrichment methods work best depends strongly on how many GO terms or other biological categories are of interest.
Combining inferences from different methods
D. R. Bickel, “Resolving conflicts between statistical methods by probability combination: Application to empirical Bayes analyses of genomic data,” Technical Report, Ottawa Institute of Systems Biology, arXiv:1111.6174 (2011). Full preprint
This paper proposes a solution to the problem of combining the results of differing statistical methods that may legitimately be used to analyze the same data set. The motivating application is the combination of two estimators of the probability of differential gene expression: one uses an empirical null distribution, and the other uses the theoretical null distribution. Since there is usually not any reliable way to predict which null distribution will perform better for a given data set and since the choice between them often has a large impact on the conclusions, the proposed hedging strategy addresses a pressing need in statistical genomics. Many other applications are also mentioned in the abstract and described in the introduction.
