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      Estimating the null distribution for conditional inference and genome-scale screening

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          Abstract

          In a novel approach to the multiple testing problem, Efron (2004; 2007) formulated estimators of the distribution of test statistics or nominal p-values under a null distribution suitable for modeling the data of thousands of unaffected genes, non-associated single-nucleotide polymorphisms, or other biological features. Estimators of the null distribution can improve not only the empirical Bayes procedure for which it was originally intended, but also many other multiple comparison procedures. Such estimators serve as the groundwork for the proposed multiple comparison procedure based on a recent frequentist method of minimizing posterior expected loss, exemplified with a non-additive loss function designed for genomic screening rather than for validation. The merit of estimating the null distribution is examined from the vantage point of conditional inference in the remainder of the paper. In a simulation study of genome-scale multiple testing, conditioning the observed confidence level on the estimated null distribution as an approximate ancillary statistic markedly improved conditional inference. To enable researchers to determine whether to rely on a particular estimated null distribution for inference or decision making, an information-theoretic score is provided that quantifies the benefit of conditioning. As the sum of the degree of ancillarity and the degree of inferential relevance, the score reflects the balance conditioning would strike between the two conflicting terms. Applications to gene expression microarray data illustrate the methods introduced.

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          Empirical Bayes Analysis of a Microarray Experiment

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            Transcriptome and selected metabolite analyses reveal multiple points of ethylene control during tomato fruit development.

            Transcriptome profiling via cDNA microarray analysis identified 869 genes that are differentially expressed in developing tomato (Solanum lycopersicum) pericarp. Parallel phenotypic and targeted metabolite comparisons were employed to inform the expression analysis. Transcript accumulation in tomato fruit was observed to be extensively coordinated and often completely dependent on ethylene. Mutation of an ethylene receptor (Never-ripe [Nr]), which reduces ethylene sensitivity and inhibits ripening, alters the expression of 37% of these 869 genes. Nr also influences fruit morphology, seed number, ascorbate accumulation, carotenoid biosynthesis, ethylene evolution, and the expression of many genes during fruit maturation, indicating that ethylene governs multiple aspects of development both prior to and during fruit ripening in tomato. Of the 869 genes identified, 628 share homology (E-value < or = 1 x 10(-10)) with known gene products or known protein domains. Of these 628 loci, 72 share homology with previously described signal transduction or transcription factors, suggesting complex regulatory control. These results demonstrate multiple points of ethylene regulatory control during tomato fruit development and provide new insights into the molecular basis of ethylene-mediated ripening.
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              Correlation and Large-Scale Simultaneous Significance Testing

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                Author and article information

                Journal
                05 October 2009
                Article
                10.1111/j.1541-0420.2010.01491.x
                0910.0745
                ecd4b4c5-578f-47fc-8096-5f8aa49fed79

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                D. R. Bickel, Estimating the null distribution to adjust observed confidence levels for genome-scale screening, Biometrics 67, 363-370 (2011)
                stat.ME math.ST stat.TH

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