## 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

## 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.

## Minimax strength of statistical evidence

D. R. Bickel, “A predictive approach to measuring the strength of statistical evidence for single and multiple comparisons,” *Canadian Journal of Statistics* **39**, 610–631 (2011). Full text | Revised preprint | 2010 draft

This paper introduces a novel approach to the multiple comparisons problem by generalizing a promising method of model selection developed by information theorists. The first two sections present that method and its main advantages over conventional approaches without burdening statisticians with unfamiliar terms from coding theory. A quantitative proteomics case study facilitates application of the new method to the analysis of data sets involving multiple biological features. The theorems describe its operating characteristics.

The cited medium-scale paper presented previous minimum description length (MDL) methods. Unlike those methods, the new MDL methods of the current paper are based on a conflation of the normalized maximum likelihood (NML) with the weighted likelihood (WL). The previous MDL methods are used in the *CJS* article for comparison with its NML/WL methods.

## Software for local false discovery rate estimation

LFDR-MLE is a suite of R functions for the estimation of local false discovery rates by maximum likelihood under a two-group parametric mixture model of test statistics.