## 5 Conclusions  
In this study, cost-benefit analysis, with the help of machine learning techniques, was utilized to estimate the benefit of upgrading the heights of Wyoming road barriers to their standards. Due to the randomness of crashes and the low volume of traffic in the state, a severe sparsity in the dataset could be observed for the frequency of barriers' crashes. The high sparsity was accompanied by severe data heterogeneity resulting from integration of various barrier types and highway systems. It is hypothesized that due to high heterogeneity and sparsity of the dataset, ignoring those shortcomings would result in erroneous and biased results. Thus, to address the issue of sparsity, the negative binomial distribution was implemented. Also, to account for the data heterogeneity, various parameters such as state highway systems, barrier types and objective clustering through FMM were considered as a hierarchy of the model. Not accounting for heterogeneity or sparsity of the data could result in biased or erroneous results. The modeling methodology was conducted in the context of the Bayesian method.  
With regard to objective clustering, the FMM was conducted and the optimum number of clusters was identified. The FMM was conducted in the context of maximum likelihood due to the label switching issue of the method in the Bayesian context. The identified clusters were assigned to each observation. In the next step a Bayesian hierarchical model with the FMM hierarchy was compared with subjective intuitive clustering, e.g., the state highway systems and barrier types. Models were compared and the model with a best assigned hierarchy was chosen. Deviance information criterion (DIC) was used for model selection.  
Predicted EPDO crashes for each year were based on interpolated traffic. The barriers' heights were changed to their optimum values and the machine learning technique was implemented again. The predicted cost for barriers with and without enhancement were summarized and the barrier optimization costs were considered. The difference in crash costs before and after height adjustments was calculated as a total benefit.  
In summary, the results indicated that after investing money to bring under-design barriers to their optimum heights, WYDOT would not only recover the invested money in 10 years but they would also expect to save more than $4 million dollars in crash savings through the optimization process of the barriers. Although the analysis highlights the interaction terms between both shoulder width and barrier heights, the shoulder width was left constant, and only barrier heights were optimized. If the constraint was set free, more benefits would have been gained by optimizing both barrier heights and shoulder width.  
This study is one of the first studies that quantifies the monetary benefit of optimizing the heights of traffic barriers. More studies are needed to quantify other aspects of traffic enhancement through machine learning techniques. The WYDOT could utilize the ranking list developed in this analysis to allocate funding to upgrade all traffic barriers in the state. The upgrade might take a few years considering the total amount of needed funding, and limited safety funds statewide.  
**Author Contributions:** K.K. funding and supervision, M.R. methodology and statistical analysis. Both authors have read and agreed to the published version of the manuscript.  
**Funding:** The authors would like to acknowledge that this work is part of project #RS03218 funded by the Wyoming Department of Transportation (WYDOT). All figures, tables are copyrighted by WYDOT.  
**Conflicts of Interest:** The authors declare no conflict of interest.