Hierarchical Bayesian Modeling for Before-and-After Studies

Hierarchical Bayesian methods are a powerful extension of commonly used empirical Bayesian methods. Bayesian methodology combines prior information with information from the data to create a posterior distribution. This fundamental principle extends to the development of Poisson hierarchical regression, which allows count data to be modeled as a function of one or more co-variates. This framework is extremely useful in before-after traffic safety studies because both the type of crash and co-variates included in the analysis may be changed in an extremely flexible manner. No calibrated factors are required, which reduces time and effort necessary for analysis. Hierarchical Bayesian methods also require fewer data in order to achieve valid results. With these distinct advantages associated with hierarchical Bayesian modeling, Departments of Transportation (DOTs) and other entities could be benefited immensely by the use of Bayesian methodology in their research. The relatively recent onset of these methods as they apply to traffic studies, however, can make implementation of new Bayesian methods seem daunting. This paper seeks to help bridge the gap between cursory familiarity with Bayesian methods and thorough understanding of the foundations of Bayesian analysis and how to apply them to traffic studies. To facilitate the presentation of Bayesian methods as they apply to before-after studies, an application evaluating the efficacy of cable barriers on Utah highways is presented. The foundational principles of Bayesian statistics discussed may be applied to essentially any situation as the fundamentals of hierarchical modeling are understood and implemented by researchers.