A study on the impact of prior distributions in Bayesian inference

Abstract

This thesis delves into the critical role that prior distributions play in Bayesian statistical analysis. Through a series of meticulously chosen practical examples, the research explores the nuanced effects of conjugate, non-informative, and hierarchical priors on Bayesian inference outcomes. The thesis begins by elucidating the theoretical foundations of Bayesian statistics, emphasizing the dynamic process of updating beliefs in light of new evidence and the pivotal importance of selecting appropriate priors. It then progresses to demonstrate, via both theoretical analysis and simulation studies, how different prior choices can lead to divergent interpretations of identical datasets. The examples range from simple applications in binomial settings to more complex scenarios involving hierarchical models, showcasing the flexibility and challenges of prior selection. Furthermore, the thesis introduces innovative methodologies for assessing the impact of priors, including the Wasserstein distance and Stein's method, offering researchers new tools for making informed decisions about prior selection. By bridging the gap between abstract statistical theory and practical application, this work contributes to a deeper understanding of Bayesian inference’s foundational principles and underscores the significance of thoughtful prior selection in shaping analytical outcomes. Through this exploration, the thesis not only advances our knowledge of statistical principles but also enhances our ability to effectively apply these principles in the quest for knowledge across various domains.