Professor of Civil Engineering, Director of Center for Road Safety, Lyles School of Civil Engineering, Purdue University, West Lafayette, IN, 47907, USA.
Accid Anal Prev. 2018 Apr;113:63-73. doi: 10.1016/j.aap.2018.01.008. Epub 2018 Mar 7.
This paper justifies the Lomax distribution for counterfactual modeling of the probability of crash given a traffic conflict. The pre-crash process leading to a conflict or a crash as the result of a failure is discussed as this conceptualization is the basis for proposing a simple model of the probability of a crash at the moment when a conflict is still progressing. Then, a model applicable to heterogeneous conditions is derived; and the model's relevance, useful properties, and limitations are discussed. The published concepts and study results that support the derived model are provided in the paper. The existing Maximum Likelihood Estimate (MLE) method and the Probability-Weighted Moments (PWM) method of estimating the probability of crash and the expected number of crashes based on the proposed theory are presented. Then, a new Single Parameter Estimation (SPE) method is proposed and evaluated with extensive Monte Carlo experiments. The performance of the MLE, PWM, and SPE methods are compared. The SPE method is found more accurate and efficient than the other two methods. Unlike the benchmark methods, the proposed method produces real estimates in each case. The most important outcome of the presented study is confirmation that traffic conflicts claimed based on sufficiently small threshold separation (such as Time to Collision) allow unbiased estimation of the expected number of crashes during the conflicts observation period. A practical procedure of estimating safety is proposed that identifies the longest suitable threshold separation for each case based on the trends in the estimation results.
本文为给定交通冲突条件下碰撞概率的反事实建模证明了 Lomax 分布的合理性。讨论了导致冲突或碰撞的碰撞前过程，因为这种概念化是提出冲突仍在进行时碰撞概率简单模型的基础。然后，推导出适用于异质条件的模型；并讨论了模型的相关性、有用特性和局限性。本文提供了支持所推导模型的已发表概念和研究结果。提出了基于所提出理论的基于最大似然估计（MLE）方法和概率加权矩（PWM）方法估计碰撞概率和预期碰撞次数的方法。然后，提出了一种新的单参数估计（SPE）方法，并通过广泛的蒙特卡罗实验进行了评估。比较了 MLE、PWM 和 SPE 方法的性能。结果表明，SPE 方法比其他两种方法更准确和高效。与基准方法不同，所提出的方法在每种情况下都产生真实的估计。本研究最重要的结果是确认基于足够小的时间间隔（如碰撞时间）的交通冲突声称允许在冲突观察期内对预期碰撞次数进行无偏估计。提出了一种实用的安全估计程序，该程序基于估计结果的趋势，为每种情况确定最长合适的时间间隔。
