A Multivariate Poisson/Gamma Model with Two- and Three-Way Covariance Structure to Construct Candidate Lists for Different Severities

• Activity Number: 628
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Kristian Schmidt*+ and Alicia L. Carriquiry and Michael D. Pawlovich
• Companies: Iowa State University and Iowa State University and Iowa Department of Transportation
• Keywords: Poisson/Gamma ; Traffic Statistics ; Bayesian statistics ; MCMC ; Multivariate Statistics

Abstract

Improving tra?c safety is a priority of Departments of Transportation nationwide. Methods to identify those sites with the highest risk potential and that may respond to interventions are of special importance, because every agency faces budgetary constraints. The initial objective of this work was to develop an accurate approach that can be used to construct candidate lists of intersections for improvement. To do so, the methodology must take into account not only the estimated expected crash frequency (or crash rate) but also the uncertainties associated with that estimate. We add a multivariate component to a Poisson/Gamma model we previously developed to account for different crash severities (i.e., Fatal, Injury, Property Damage Only). Simultaneously modeling different severities preserves the correlation structure in the data and also allows for 'borrowing strength' between different severity types (i.e., we are able to model rarely occuring fatal crashes with less uncertainty and bias than in the univariate case). In contrast to many other authors, we introduce a model that allows for two- and three-way covariance structures.