Traffic crash datasets are often marred by the presence of anomalous data points, commonly referred to as outliers. These outliers can have a profound impact on the results obtained through the application of traditional methods such as logit and probit models, commonly used in the domain of traffic safety analysis, resulting in biased and unreliable estimates. To mitigate this issue, this study introduces a robust Bayesian regression approach, the robit model, which utilizes a heavy-tailed Student's t distribution to replace the link function of these thin-tailed distributions, effectively reducing the influence of outliers on the analysis. Furthermore, a sandwich algorithm based on data augmentation is proposed to enhance the estimation efficiency of posteriors. The proposed model is rigorously tested using a dataset of tunnel crashes, and the results demonstrate its efficiency, robustness, and superior performance compared to traditional methods. The study also reveals that several factors such as night and speeding have a significant impact on the injury severity of tunnel crashes. This research provides a comprehensive understanding of the outliers treatment methods in traffic safety studies and offers valuable recommendations for the development of appropriate countermeasures to effectively prevent severe injuries in tunnel crashes.