Application of Bayesian Hierarchical Negative Binomial Finite Mixture Model for Cost-Benefit Analysis of Barriers Optimization, Accounting for Severe Heterogeneity

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The Wyoming Department of Transportation (WYDOT) initiated a project to optimize the heights of barriers that are not satisfying the barrier design criteria, while prioritizing them based on an ability to achieve higher monetary benefits. The equivalent property damage only (EPDO) was used in this study to account for both aspects of crash frequency and severity. Data of this type are known to have overdispersion, that is having a variance greater than the mean. Thus, a negative binomial model was implemented to address the over-dispersion issue of the dataset. Another challenge of the dataset used in this study was the heterogeneity of the dataset. The data heterogeneity resulted from various factors such as data being aggregated across two highway systems, and the presence of two barrier types in the whole state. Thus, it is not practical to assign a subjective hierarchy such as a highway system or barrier types to address the issue of severe heterogeneity in the dataset. Under these conditions, a finite mixture model (FMM) was implemented to find a best distribution parameter to characterize the observations. With this technique, after the optimum number of mixtures was identified, those clusters were assigned to various observations. However, previous studies mostly employed just the finite mixture model (FMM), with various distributions, to account for unobserved heterogeneity. The problem with the FMM approach is that it results in a loss of information: for instance, it would come up with N number of equations, where each result would use only part of the whole dataset. On the other hand, some studies used a subjective hierarchy to account for the heterogeneity in the dataset, such as the effect of seasonality or highway system; however, those subjective hierarchies might not account for the optimum heterogeneity in the dataset. Thus, we implement a new methodology, the Bayesian Hierarchical Finite Mixture (BHFMM) to employ the FMM without losing information, while also accounting for the heterogeneity in the dataset, by considering objective and unbiased hierarchies. As the Bayesian technique has the shortcoming of labeling the observations due to label switching; the FMM parameters were estimated by maximum likelihood technique. Results of the identified model were converted to an equation for implementation of machine learning techniques. The heights were optimized to an optimal value and the EPDO was predicted based on the changes. The results of the cost–benefit analysis indicated that after spending about 4 million dollars, the WYDOT would not only recover the expenses, but could also expect to save more than $4 million additional dollars through traffic barrier crash reduction.