Evaluating the Relationship Between Prior Distributions and Posterior Estimates in Bayesian Modeling Frameworks

Posted: Mar 03, 2015

• Nathan Howard
• Nicholas Diaz
• Nora Hayes

Abstract

Bayesian statistical methods have experienced remarkable growth in application across scientific disciplines, driven by their principled approach to uncertainty quantification and ability to incorporate prior knowledge. The fundamental Bayesian framework operates through the coherent updating of prior beliefs in light of observed data, producing posterior distributions that form the basis for statistical inference. While the theoretical foundations of Bayesian analysis are well-established, the practical implementation often hinges on the specification of prior distributions, which represent the researcher's initial beliefs or external information before observing the data. The relationship between prior specification and resulting posterior estimates constitutes a critical yet underexplored dimension of Bayesian methodology.