Car following model is an important part in traffic modelling and has attracted a lot of attentions in the literature. As the proposed car following models become more complex with more components, reliably estimating their parameters becomes crucial to enhance model predictive performance. While most studies adopt an optimisation-based approach for parameters estimation, we present a statistically rigorous method that quantifies uncertainty of the estimates. We present a Bayesian approach to estimate parameters using the popular Gipps’ car following model as demonstration, which allows proper uncertainty quantification and propagation. Since the parameters of the car following model enter the statistical model through the solution of a delay-differential equation, the posterior is analytically intractable so we implemented an adaptive Markov Chain Monte Carlo algorithm to sample from it. Our results show that predictive uncertainty using a point estimator versus a full Bayesian approach are similar with sufficient data. In the absence of adequate data, the former can make over-confident predictions while such uncertainty is more appropriately incorporated in a Bayesian framework. Furthermore, we found that the congested flow parameters in the Gipps’ car following model are strongly correlated in the posterior, which not only causes issues for sampling efficiency but more so suggests the potential ineffectiveness of a point estimator in an optimisation-based approach. Lastly, an application of the Bayesian approach to a car following episode in the NGISM dataset is presented.

中文翻译：

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贝叶斯框架中吉普斯汽车跟随模型的参数估计

汽车跟随模型是交通建模的重要组成部分，在文献中引起了广泛的关注。随着所提出的汽车跟随模型变得越来越复杂，组件越来越多，可靠地估计其参数对于增强模型预测性能变得至关重要。虽然大多数研究采用基于优化的方法进行参数估计，但我们提出了一种统计上严格的方法来量化估计的不确定性。我们提出了一种贝叶斯方法来估计参数，使用流行的吉普斯汽车跟随模型作为演示，该模型允许适当的不确定性量化和传播。由于跟车模型的参数通过求解时滞微分方程进入统计模型，后验分析起来比较困难，因此我们实现了自适应马尔可夫链蒙特卡罗算法来从中采样。我们的结果表明，在数据充足的情况下，使用点估计器与完整贝叶斯方法的预测不确定性相似。在缺乏足够数据的情况下，前者可能会做出过于自信的预测，而这种不确定性更适合纳入贝叶斯框架。此外，我们发现吉普斯汽车跟随模型中的拥塞流参数在后验中具有很强的相关性，这不仅会导致采样效率问题，而且更表明基于优化的方法中点估计器的潜在无效性。最后，介绍了贝叶斯方法在 NGISM 数据集中汽车跟踪事件中的应用。