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Archive for the ‘preprints’ Category

Estimating probabilities of enrichment

4 January 2012 Leave a comment

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

28 November 2011 Leave a comment

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.

Degree of caution in inference

26 September 2011 Leave a comment

D. R. Bickel, “Controlling the degree of caution in statistical inference with the Bayesian and frequentist approaches as opposite extremes,” Technical Report, Ottawa Institute of Systems Biology, arXiv:1109.5278 (2011). Full preprint

This paper’s framework of statistical inference is intended to facilitate the development of new methods to bridge the gap between the frequentist and Bayesian approaches. Three concrete examples illustrate how such intermediate methods can leverage strengths of the two extreme approaches.

All-scale FDR estimation

24 June 2011 Leave a comment

D. R. Bickel, “Simple estimators of false discovery rates given as few as one or two p-values without strong parametric assumptions,” Technical Report, Ottawa Institute of Systems Biology, arXiv:1106.4490 (2011). Full preprint

To address multiple comparison problems in small-to-high-dimensional biology, this paper introduces novel estimators of the local false discovery rate (LFDR), reports their main properties, and illustrates their use with proteomics data. Unlike previous LFDR estimators, the new estimators have all of the following advantages:

  1. proven asymptotic conservatism;
  2. simplicity of calculation without the tuning of smoothing parameters;
  3. no strong parametric assumptions;
  4. applicability to very small numbers of hypotheses as well as to very large numbers of hypotheses.

Unknown Bayes factor approximation

5 April 2011 Leave a comment

D. R. Bickel, “Measuring support for a hypothesis about a random parameter without estimating its unknown prior,” Technical Report, Ottawa Institute of Systems Biology, arXiv:1101.0305 (2011). Full preprint

Small-scale inference

5 April 2011 Leave a comment

D. R. Bickel, “Small-scale inference: Empirical Bayes and confidence methods for as few as a single comparison,” Technical Report, Ottawa Institute of Systems Biology, arXiv:1104.0341 (2011). Full preprint

Parametric empirical Bayes methods of estimating the local false discovery rate by maximum likelihood apply not only to the multiple comparison settings for which they were developed, but, with a simple modification, also to small numbers of comparisons. In fact, data for a single comparison are sufficient under broad conditions, as seen from applications to measurements of the abundance levels of 20 proteins and from simulation studies with confidence-based inference as the competitor.

Confidence intervals for semi-parametric empirical Bayes

7 January 2011 2 comments

D. R. Bickel, “Large-scale interval and point estimates from an empirical Bayes extension of confidence posteriors,” Technical Report, Ottawa Institute of Systems Biology, arXiv:1012.6033 (2010). Full preprint

To address multiple comparison problems in high-dimensional biology, this paper introduces shrunken point estimates for feature prioritization and shrunken confidence intervals to indicate the uncertainty of the point estimates. The new point and interval estimates are applied to gene expression data and are found to be conservative by simulation, as expected from limiting cases. Unlike the parametric empirical Bayes estimates, the new estimates are compatible with the semi-parametric approach to local false discovery rate estimation that has been extensively developed and applied over the last decade. This is carried out by replacing strong parametric assumptions with the confidence posterior theory of papers in the presses of Biometrics and Communications in Statistics — Theory and Methods.

Quantifying evidence for enrichment

7 January 2011 Leave a comment

Z. Yang and D. R. Bickel, “Minimum description length measures of evidence for enrichment,” Technical Report, Ottawa Institute of Systems Biology, COBRA Preprint Series, Article 76, available at biostats.bepress.com/cobra/ps/art76 (2010). Full preprint

Quantifying evidence for genetic association

30 November 2010 Leave a comment

Y. Yang and D. R. Bickel, “Minimum description length and empirical Bayes methods of identifying SNPs associated with disease,” Technical Report, Ottawa Institute of Systems Biology, COBRA Preprint Series, Article 74, available at biostats.bepress.com/cobra/ps/art74 (2010).

This manuscript adapts two new evidential, information-theoretic methods to the problem of detecting SNPs associated with disease on the basis of genome-wide association data. Both an application to coronary artery disease and an extensive set of simulation studies indicate that these parametric methods tend to be more reliable than a popular semi-parametric approach to estimating local false discovery rates. In addition, the paper reports that one of the two novel methods performs better than the other.

The abstract and the discussion section of the preprint provide more detailed summaries.

Normalized maximum weighted likelihood

8 October 2010 1 comment

D. R. Bickel, “Statistical inference optimized with respect to the observed sample for single or multiple comparisons,” Technical Report, Ottawa Institute of Systems Biology, arXiv:1010.0694 (2010). Full preprint