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From Bayes calculation to efficient ...

Han, Han.

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From Bayes calculation to efficient integration of studies: Three statistical problems.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	From Bayes calculation to efficient integration of studies: Three statistical problems./
Author:	Han, Han.
Description:	117 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-05(E), Section: B.
Contained By:	Dissertation Abstracts International74-05B(E).
Subject:	Biology, Genetics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3548237
ISBN:	9781267835147

From Bayes calculation to efficient integration of studies: Three statistical problems.
Han, Han.

From Bayes calculation to efficient integration of studies: Three statistical problems. - 117 p.

Source: Dissertation Abstracts International, Volume: 74-05(E), Section: B.

Thesis (Ph.D.)--The University of Chicago, 2012.

This thesis contains three main parts. The first part discusses a theoretical development in Bayes calculations, while the latter two parts focus on statistical methods with the applications to genetics.

ISBN: 9781267835147Subjects--Topical Terms:

1017730
Biology, Genetics.

From Bayes calculation to efficient integration of studies: Three statistical problems.
LDR:05943nam 2200337 4500 001 1957621
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008 150210s2012 ||||||||||||||||| ||eng d
020 $a 9781267835147
035 $a (UMI)AAI3548237
035 $a AAI3548237
040 $a UMI $c UMI
100 1 $a Han, Han. $3 1033727
245 1 0 $a From Bayes calculation to efficient integration of studies: Three statistical problems.
300 $a 117 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-05(E), Section: B.
500 $a Advisers: Peter McCullagh; Dan Nicolae.
502 $a Thesis (Ph.D.)--The University of Chicago, 2012.
520 $a This thesis contains three main parts. The first part discusses a theoretical development in Bayes calculations, while the latter two parts focus on statistical methods with the applications to genetics.
520 $a In the first part, we establish the first Bayes's theorem for improper mixtures. Although Bayes's theorem demands a prior that is a probability distribution on the parameter space, the calculus associated with Bayes's theorem sometimes generates sensible procedures from improper priors, Pitman's estimator being a good example. However, improper priors may also lead to Bayes procedures that are paradoxical or otherwise unsatisfactory, prompting some authors to insist that all priors be proper. This work begins with the observation that an improper measure on &THgr; satisfying Kingman's countability condition is in fact a probability distribution on the power set. We show how to extend a model in such a way that the extended parameter space is the power set. Under an additional finiteness condition, which is needed for the existence of a sampling region, the conditions for Bayes's theorem are satisfied by the extension. Lack of interference ensures that the posterior distribution in the extended space is compatible with the original parameterspace. Provided that the key finiteness condition is satisfied, this probabilistic analysis of the extended model may be interpreted as a vindication of improper Bayes procedures derived from the original model.
520 $a In the second part, we propose a new meta-analysis approach to identify common predictors from multiple related studies. Identifying molecular signatures for complex diseases such as breast cancer remains one major objective in gene expression studies. Commonly used strategies mainly investigate one gene expression study at a time, where the combination of small sample size and a large number of genetic predictors often leads to low detection power and to inaccuracy in the estimation of the set of relevant genes. We present here methodology for improving the power of identifying gene signatures by combining summary statistics from several relevant studies. The group lasso proposed by Yuan and Lin [2006] could be used for this purpose, where the regression coefficients of the same predictor across multiple studies naturally form a group. Their approach is challenged when predictors have heterogeneous effects or effect direction coherence. Motivated by these issues, we introduce a nonparametric approach called Meta-Rank Selection. Our three-step approach first infers the rank of a predictor and its marginal correlation with the response in each individual study, combines the two scores to form a consensus ranking path of all predictors, then selects the relevant predictors along the consensus ranking path. We present theoretical properties of Meta-Rank Selection and use simulations to compare its performance with other methods such as the group lasso. We also discuss its extensions, including ways to incorporate effect direction coherence and tools to deal with strong correlations among predictors. We apply Meta-Rank Selection in a real data analysis to identify common gene signatures from multiple gene expression studies.
520 $a In the third part, we develop a new nonparametric association test to identify pleiotropic eQTLs. Identifying functional genetic variation remains a central challenge in human genetics. A popular tool for functional SNP identification is the search for variants that affect gene expression levels, called expression quantitative trait loci (eQTLs). Common approaches mainly investigate the association between one genetic marker and one expression trait, where the combination of small effect sizes and large number of statistical tests often leads to low power in detecting association. We present here methodology for improving the power of association tests by carefully modeling the molecular architecture of the traits of interest. Our approach tests association between one genetic marker and a set of gene expression phenotypes that are regulated by a common intermediate phenotype such as a transcription factor. The genetic marker that influences multiple phenotypic traits is called a pleiotropic eQTL. It addresses two challenges in detecting association under this scenario: potential nonlinear relationships between the latent (unobserved) variable and the expression traits, and the computational burden from investigating millions of genetic variants. Our nonparametric approach first infers the ranks of the unobserved realizations of the latent variable then conducts a rank-based association test. We present some theoretical results of the test and compare its performance with other tests using simulations. We also discuss other applications of our proposed methodology including the detection of pleiotropic effects in multivariate human phenotypes.
590 $a School code: 0330.
650 4 $a Biology, Genetics. $3 1017730
650 4 $a Statistics. $3 517247
690 $a 0369
690 $a 0463
710 2 $a The University of Chicago. $b Statistics. $3 1673632
773 0 $t Dissertation Abstracts International $g 74-05B(E).
790 1 0 $a McCullagh, Peter, $e advisor
790 1 0 $a Nicolae, Dan, $e advisor
790 1 0 $a Stephens, Matthew $e committee member
790 $a 0330
791 $a Ph.D.
792 $a 2012
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3548237