Application of Bayesian Semi-Parametric and Hierarchical Models for Analyzing Dispersed Traffic Barriers Crash Data

Mahdi Rezapour1, *, Khaled Ksaibati1
1 Department Civil Engineering, Wyoming Technology Transfer Center, Wyoming WYT2, United States

Article Metrics

CrossRef Citations:
Total Statistics:

Full-Text HTML Views: 366
Abstract HTML Views: 258
PDF Downloads: 119
ePub Downloads: 78
Total Views/Downloads: 821
Unique Statistics:

Full-Text HTML Views: 235
Abstract HTML Views: 179
PDF Downloads: 96
ePub Downloads: 60
Total Views/Downloads: 570

Creative Commons License
© 2022 Rezapour and Ksaibati

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Civil engineering, WYT2, United States; E-mail:



Despite the traffic barriers effectiveness in reduction of the severity of run-off road crashes, the severity of barrier crashes still accounts for a significant fraction of road fatalities. Although extensive research has already been conducted in studying traffic barrier crashes, those studies mostly either consider the severity or frequency of crashes. Here, the equivalent property damage only (EPDO) was used to account for both aspects of crashes. While modeling EPDO crashes, there are challenges associated with that type of dataset including its sparse distribution, and the presence of heterogeneity in the dataset due to aggregation of various crash types.


Ignoring the sparse nature of the data might result in biased or even erroneous results. Thus, in this study we identify factors to barriers EPDO crashes while considering the discussed challenges. Those consideration are especially important as in the next step we will employ the modeling results for conducting the cost-benefit analysis. Two main methods were considered in this study to address the discussed challenges including parametric and non-parametric Bayesian hierarchical models. A semiparametric Bayesian approach was used to relax the normality assumption by using a mixture of multivariate Dirichlet prior, defining a flexible nonparametric model for the random effects’ distribution, and using grouping to account for the heterogeneity due to the structure of the dataset. On the other hand, Bayesian hierarchical models with two distributions of Poisson and negative binomial with similar levels of hierarchy were considered. These models were chosen as closest models to the Bayesian semiparametric model. The incorporated models were compared in terms of deviance information criterion (DIC).

Results and Discussion:

The results highlighted that although the semi-parametric method outperforms the Bayesian hierarchical model with Poisson distribution, the Bayesian hierarchical model with negative binomial (NB) distribution outperform the semi-parametric model. The findings might be related to the severe sparse nature of the EPDO, which cannot optimally be accounted by semiparametric approach, and the model needs more flexibility.


It was found that being unrestrained, driving in interstate system, driving in clear weather, light conditions, and driving in a higher traffic all increase the likelihood of EPDO crashes. Also, while some predictors were significant in less accommodative models of semi-parametric or Poisson models, they were not for Negative binomial model.

Keywords: Bayesian semiparametric model, Bayesian hierarchical model, Sparse data, DIC, Equivalent Property Damage Only (EPDO), Traffic barrier crashes, Traffic safety .