UC Davis

This dissertation is a collection of three papers I wrote during my time in graduate school. Each proposes a novel way in which a Bayesian statistical technique may be applied or conceptualized for the purpose of better aligning statistical hypotheses and research aims, or improving upon the status quo with respect to the application of statistical methods in psychological science. On a personal note, these articles represent endeavors that pushed my intellectual limits and challenged my grit and mettle. The articles are presented as chapters, and in the chronological order in which they were written. I hope this reflects my thought process and growth throughout my time in graduate school. The first chapter presents a framework for integrating exploratory and confirmatory analyses in psychological network research. It is argued that while network analysis has been proposed as a tool for hypothesis generation, there is untapped potential for confirmatory hypothesis testing. We suggest using Bayesian Gaussian graphical models to first generate and then test ordered hypotheses based on the conditional (in)dependence structure of psychological networks.

The second chapter proposes the use of the Bayesian bootstrap method to estimate various correlation coefficients commonly used in the social-behavioral sciences. We demonstrate how the Bayesian bootstrap can be used to estimate Pearson's, Spearman's, Gaussian rank, Kendall's $\tau$, and polychoric correlations. We also describe a method for comparing correlations and evaluating null associations among the estimated correlations.

Finally, in an effort to provide a more nuanced understanding of individual differences than standard approaches, the third chapter explores the spike-and-slab prior distribution for random effect selection in mixed-effects models. Simulation studies were conducted to evaluate the spike-and-slab prior in accurately distinguishing ``average'' and ``non-average'' individuals. The results highlight the spike-and-slab prior's ability to identify individual differences, even in situations with low between-person variance. This dissertation concludes by offering some discussion on why Bayesian analyses are more flexible than standard approaches, and how this flexibility can lead to higher-quality inferences in psychological science.