  Accurately forecasting 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.
