<p> Shrinkage procedures have played an important role in helping improve estimation accuracy for a variety of applications. In genomics studies, the gene-specific sample statistics are usually noisy, especially when sample size is limited. Hence some shrinkage methods (e.g. <i>limma</i>) have been proposed to increase statistical power in identifying differentially expressed genes. Motivated by the success of shrinkage methods, Stephens (2016) proposed a novel approach, Adaptive Shrinkage (<i>ash</i>) for large-scale hypothesis testing including false discovery rate and effect size estimation, based on the fundamental “unimodal assumption” (UA) that the distribution of the actual unobserved effects has a single mode. </p><p> Even though <i>ash</i> primarily dealt with normal or student-t distributed observations, the idea of UA can be widely applied to other types of data. In this dissertation, we propose a general flexible Bayesian shrinkage framework based on UA, which is easily applicable to a wide range of settings. This framework allows us to deal with data involving other noise distributions (gamma, F, Poisson, binomial, etc.). We illustrate its flexibility in a variety of genomics applications including: differential gene expression analysis on RNA-seq data; comparison between bulk RNA-seq and single cell RNA-seq data; gene expression distribution deconvolution for single cell RNA-seq data, etc. </p><p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:10974422 |
| Date | 01 January 2019 |
| Creators | Lu, Mengyin |
| Publisher | The University of Chicago |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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