To Bayes or Not to Bayes, From Whether to When: Applications of Bayesian Methodology to Modeling

Abstract

This article presents relevant research on Bayesian methods and their major applications to modeling in an effort to lay out differences between the frequentist and Bayesian paradigms and to look at the practical implications of these differences. Before research is reviewed, basic tenets and methods of the Bayesian approach to modeling are presented and contrasted with basic estimation results from a frequentist perspective. It is argued that Bayesian methods have become a viable alternative to traditional maximum likelihood-based estimation techniques and may be the only solution for more complex psychometric data structures. Hence, neither the applied nor the theoretical measurement community can afford to neglect the exciting new possibilities that have opened up on the psychometric horizon.