Statistical Inference for Transit System Origin-Destination Matrices

We consider inference for the matrix of origin-destination (O-D) trip rates for a transit system, based on counts of the passengers boarding and alighting at each stop. The observed data provide only indirect information about the O-D rates through a highly indeterminate system of linear equations. Enumeration of the solution set of feasible trips is necessary to calculate the model likelihood, but this would be computationally prohibitive for even moderately large systems. We therefore adopt a sampling-based Bayesian approach. Existing work on the wider problem of O-D traffic rate estimation for general transport networks has failed to produce an efficient sampling methodology for sizeable applications; however, we were able to derive a suitable Markov chain Monte Carlo algorithm by generating candidate trip vectors directly from the feasible set using a Markov model of passenger behavior. The resulting sampler moves freely around the posterior support without the need for any explicit specification of the feasible trip set. This methodology is applicable regardless of whether or not the O-D matrix is assumed to have any given structure. We illustrate our methods with a case study on O-D trip rates for a bus service in San Francisco Bay.