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Understanding correlation between influential factors and insurance losses is beneficial for insurers to accurately price and modify the bonus-malus system. Although there have been a certain number of achievements in insurance losses and claims modeling, limited efforts focus on exploring the relative role of accidents characteristics in insurance losses. The primary objective of this study is to evaluate the influential priority of transit accidents attributes, such as the time, location and type of accidents. Based on the dataset from Washington State Transit Insurance Pool (WSTIP) in USA, we implement several key algorithms to achieve the objectives. First, K-means algorithm contributes to cluster the insurance loss data into 6 intervals; second, Grey Relational Analysis (GCA) model is applied to calculate grey relational grades of the influential factors in each interval; in addition, we implement Naive Bayes model to compute the posterior probability of factors values falling in each interval. The results show that the time, location and type of accidents significantly influence the insurance loss in the first five intervals, but their grey relational grades show no significantly difference. In the last interval which represents the highest insurance loss, the grey relational grade of the time is significant higher than that of the location and type of accidents. For each value of the time and location, the insurance loss most likely falls in the first and second intervals which refers to the lower loss. However, for accidents between buses and non-motorized road users, the probability of insurance loss falling in the interval 6 tends to be highest. [ABSTRACT FROM AUTHOR]