公交线路路段行程时间相关性的贝叶斯推断
Bayesian inference for link travel time correlation of a bus route
AI总结：
本文提出一种贝叶斯高斯模型及Gibbs采样框架，通过整合多线路不完整数据克服小样本问题，准确估计公交线路路段行程时间的复杂相关矩阵，并验证了其在概率预测中的应用。
摘要：
公交线路路段行程时间相关性的估计对许多公交运营应用至关重要，如时刻表调度、行程时间预测和公交服务评估/改进。以往的大多数研究要么依赖独立假设，要么依赖简化的局部空间相关结构。然而在现实世界中，公交线路的路段行程时间可能表现出复杂的相关结构，如长程相关性、负相关性和时变相关性。因此，在引入强假设之前，必须从真实公交运营数据中实证量化和考察路段行程时间的相关结构。为此，本文开发了一种贝叶斯高斯模型，利用类似智能卡的数据来估计公交线路的路段行程时间相关矩阵。该方法通过借用/整合来自其他公交线路的不完整观测值（即具有缺失/不规则值和重叠路段），克服了相关矩阵估计中的小样本量问题。接着，我们提出了一种高效的Gibbs采样框架，对缺失和不规则值进行边缘化处理，并获得相关矩阵的后验分布。我们进行了三个数值实验来评估模型性能。首先进行合成实验，结果表明所提方法能对行程时间相关性进行带有可信区间的准确估计。接着，使用智能卡数据在真实公交线路上进行实验，结果表明该线路上同时存在局部和长程相关性。最后，我们展示了使用估计的协方差矩阵对路段和行程时间进行概率预测的应用。
英文摘要：
Estimation of link travel time correlation of a bus route is essential to many bus operation applications, such as timetable scheduling, travel time forecasting and transit service assessment/improvement. Most previous studies rely on either independent assumptions or simplified local spatial correlation structures. In the real world, however, link travel time on a bus route could exhibit complex correlation structures, such as long-range correlations, negative correlations, and time-varying correlations. Therefore, before introducing strong assumptions, it is essential to empirically quantify and examine the correlation structure of link travel time from real-world bus operation data. To this end, this paper develops a Bayesian Gaussian model to estimate the link travel time correlation matrix of a bus route using smart-card-like data. Our method overcomes the small-sample-size problem in correlation matrix estimation by borrowing/integrating those incomplete observations (i.e., with missing/ragged values and overlapped link segments) from other bus routes. Next, we propose an efficient Gibbs sampling framework to marginalize over the missing and ragged values and obtain the posterior distribution of the correlation matrix. Three numerical experiments are conducted to evaluate model performance. We first conduct a synthetic experiment and our results show that the proposed method produces an accurate estimation for travel time correlations with credible intervals. Next, we perform experiments on a real-world bus route with smart card data; our results show that both local and long-range correlations exist on this bus route. Finally, we demonstrate an application of using the estimated covariance matrix to make probabilistic forecasting of link and trip travel time.
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