Xinlei Wang, Yuqui Yang, Guanghua Xiao
When conducting statistical analysis in the Bayesian paradigm, the most critical decision made by the researcher is the identification of a prior distribution for a parameter. Despite the mathematical soundness of the Bayesian approach, a wrongly specified prior can lead to biased and incorrect results. To avoid this, prior distributions should be based on real data, which are easily accessible in the "big data" era. This dissertation explores two applications of Bayesian hierarchical modelling that incorporate information obtained from a meta-analysis.
The first of these applications is in the normalization of genomics data, specifically for nanostring nCounter datasets. A meta-analysis of 13 nCounter datasets were used to identify informative prior distributions, which were then incorporated into RCRnorm, a leading normalization procedure for nCounter data that utilizes a Bayesian hierarchical model. With the new prior and other structural changes applied to the underlying model, the new normalization approach "MetaNorm", improves on its predecessor with faster speed, better convergence and stabilized estimation, even when normalizing lower-quality datasets.
The second application covers a novel sample-size determination method for one and two-sample t-tests. This novel methodology uses an empirical Bayes approach to construct a posterior predictive distribution for the variance estimate, based on data from previous studies. Simulations and empirical studies demonstrate that this methodology outperforms other aggregate approaches (simple average, weighted average, median) in variance estimation for SSD, especially in meta-analyses with large disparities in sample size and variance. Thus, it offers a robust and practical solution for sample size determination in t-tests.
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Barth, Jackson, "Development of Bayesian Hierarchical Methods involving Meta-Analysis" (2023). Statistical Science Theses and Dissertations. 32.