Full Bayesian models for paired RNA-seq data and Bayesian equivalence test

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] "In my doctorate research, I have developed Bayesian models to analyze the paired RNAseq data for different types of design. The developed methods are especially of important practice for gene expression analysis using high throughput read-count data. I also proposed and studied a Bayesian test procedure for the equivalence test with parameter margin, which has a wide range of applications in pharmaceutical statistics. In the first part of my dissertation, I presented a full hierarchical Bayesian model (PairedFB) for the paired RNA-seq count data that accounts for variation of treatment effect among pairs and controls the FDR through the posterior expected FDR. The approach was shown to be able to control FDR at nominal levels and obtain slightly higher power than other methods when their actual FDRs are comparable. The real data analysis also indicates the model tends to find more biologically significant genes. In the second part of my dissertation, I extended the Bayesian model in the first part to the differential expression analysis under multiple conditions (e.g., time points, genotype, etc.). Specifically, I developed a Bayesian partitioning model that jointly models all the possible combinations of gene expression status with the use of the "inverse moment nonlocal prior". Furthermore, I modified the posterior expected FDR under the multiple groups situation so that FDR could be controlled for each group of gene expression patterns. I demonstrated that the proposed model is capable of controlling FDR under nominal levels for each combination of expression patterns, and obtaining satisfactory power even when equivalent expression testing is involved. In the last part of my dissertation, I proposed a Bayesian approach to perform the equivalence test with parameter margin. The properties of posterior distribution of parameter of interest were studied and its frequentist properties were evaluated in terms of type I error and power comparing with other frequentist methods. The developed Bayesian test procedure was shown to control type I error close to 5 percent and obtain higher power than currently best frequentist test. Using the example dataset, I demonstrated that the proposed Bayesian test could provide unique and intuitive post-experimental evidence of supporting one hypothesis in addition to reporting the dichotomized decision." --p. 192