Archive for the ‘complexity’ Category

Optimal strength of evidence

13 February 2013 Leave a comment

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

13 February 2013 Comments off

Local FDR estimation for low-dimensional data

18 October 2012 Leave a comment

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


This article describes estimators of local false discovery rates, compares their biases for small-scale inference, and illustrates the methods using a quantitative proteomics data set. In addition, theoretical results are presented in the appendices.

How to combine statistical methods

29 August 2012 1 comment

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

Cover image

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.

Minimax strength of statistical evidence

24 November 2011 Leave a comment

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.