Accurate forecasting of bus travel time and passenger occupancy with uncertainty is essential for both travelers and transit agencies/operators. However, existing approaches to forecasting bus travel time and passenger occupancy mainly rely on deterministic models, providing only point estimates. In this paper, we develop a Bayesian Markov regime-switching vector autoregressive model to jointly forecast both bus travel time and passenger occupancy with uncertainty. The proposed approach naturally captures the intricate interactions among adjacent buses and adapts to the multimodality and skewness of real-world bus travel time and passenger occupancy observations. We develop an efficient Markov chain Monte Carlo (MCMC) sampling algorithm to approximate the resultant joint posterior distribution of the parameter vector. With this framework, the estimation of downstream bus travel time and passenger occupancy is transformed into a multivariate time series forecasting problem conditional on partially observed outcomes. Experimental validation using real-world data demonstrates the superiority of our proposed model in terms of both predictive means and uncertainty quantification compared to the Bayesian Gaussian mixture model.

中文翻译：

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使用贝叶斯马尔可夫机制切换向量自回归对公交车行驶时间和乘客占用率进行条件预测


准确预测公交车行驶时间和乘客占用率，对于旅客和公交机构/运营商来说都至关重要。然而，预测公交车行驶时间和乘客占用率的现有方法主要依赖于确定性模型，仅提供点估计。在本文中，我们开发了一个贝叶斯马尔可夫机制切换向量自回归模型，以共同预测具有不确定性的公交车旅行时间和乘客占用率。所提出的方法自然而然地捕捉了相邻公交车之间错综复杂的交互，并适应了现实世界公交车行驶时间和乘客占用观察的多模态和偏度。我们开发了一种高效的马尔可夫链蒙特卡洛 （MCMC） 采样算法来近似参数向量的结果联合后验分布。有了这个框架，对下游公交车行驶时间和乘客占用率的估计被转化为一个以部分观察到的结果为条件的多变量时间序列预测问题。使用真实世界数据的实验验证表明，与贝叶斯高斯混合模型相比，我们提出的模型在预测均值和不确定性量化方面都具有优越性。