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：起讫点（OD）需求矩阵对公交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变贝叶斯模型，旨在根据公交站点的上下车客流数据，在单车次层面估计公交OD矩阵。我们的方法首先通过由下车概率参数化的多项分布，对给定上车站点后后续站点的下车乘客数量进行建模。针对问题的大规模特性，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变矩阵，从而显著减少参数数量。为在参数中进一步编码时间平滑结构，我们对时变因子矩阵的列施加高斯过程先验。在模型推断方面，我们开发了基于马尔可夫链蒙特卡洛（MCMC）方法的两阶段算法。第一阶段使用基于马尔可夫模型的提议分布，通过Metropolis-Hastings采样算法在给定模型参数条件下对潜OD矩阵进行采样；第二阶段则使用切片采样和椭圆切片采样算法在给定潜OD矩阵条件下对模型参数进行采样。我们使用从三条不同站点数量的公交线路采集的实际数据评估所提模型，结果表明该模型能够实现准确的后验均值估计，且性能优于广泛使用的迭代比例拟合（IPF）方法。此外，本模型能为OD需求矩阵提供不确定性量化，从而有益于众多需要稳健决策的下游规划与运营任务。