Origin-destination (OD) demand matrices are crucial for transit agencies to design and operate transit systems. This paper presents a novel temporal Bayesian model designed to estimate transit OD matrices at the individual bus-journey level from boarding/alighting counts at bus stops. Our approach begins by modeling the number of alighting passengers at subsequent bus stops, given a boarding stop, through a multinomial distribution parameterized by alighting probabilities. Given the large scale of the problem, we generate alighting probabilities with a latent variable matrix and factorize it into a mapping matrix and a temporal matrix, thereby substantially reducing the number of parameters. To further encode a temporally-smooth structure in the parameters, we impose a Gaussian process prior on the columns of the temporal factor matrix. For model inference, we develop a two-stage algorithm with the Markov chain Monte Carlo (MCMC) method. In the first stage, latent OD matrices are sampled conditional on model parameters using a Metropolis-Hastings sampling algorithm with a Markov model-based proposal distribution. In the second stage, we sample model parameters conditional on latent OD matrices using slice and elliptical slice sampling algorithms. We assess the proposed model using real-world data collected from three bus routes with varying numbers of stops, and the results demonstrate that our model achieves accurate posterior mean estimation and outperforms the widely used iterative proportional fitting (IPF) method. Additionally, our model can provide uncertainty quantification for the OD demand matrices, thus benefiting many downstream planning/operational tasks that require robust decisions.

翻译：起讫（OD）需求矩阵对于公共交通运营机构设计和运营公交系统至关重要。本文提出一种新颖的时间贝叶斯模型，旨在从公交站点的上车/下车人数推断单个公交行程级别的OD矩阵。该方法首先通过多项式分布（参数化为下车概率）对给定上车站点后后续车站的下车乘客数量进行建模。针对问题规模较大的特点，我们通过潜变量矩阵生成下车概率，并将其分解为映射矩阵和时间矩阵，从而大幅减少参数数量。为在参数中进一步编码时间平滑结构，我们对时间因子矩阵的各列施加高斯过程先验。在模型推断方面，我们开发了一种基于马尔可夫链蒙特卡洛（MCMC）方法的两阶段算法：第一阶段，通过使用基于马尔可夫模型建议分布的Metropolis-Hastings采样算法，在给定模型参数的条件下对潜OD矩阵进行采样；第二阶段，通过切片采样和椭圆切片采样算法，在给定潜OD矩阵的条件下对模型参数进行采样。我们利用三条不同站点数量的公交线路实测数据对模型进行验证，结果表明该模型能够实现精准的后验均值估计，并优于广泛使用的迭代比例拟合（IPF）方法。此外，该模型可为OD需求矩阵提供不确定性量化，从而为需要稳健决策的下游规划/运营任务提供支撑。