A Bayesian Statistical Approach for Inference on Static Origin–Destination Matrices in Transportation Studies

We address the problem of static origin–destination matrix reconstruction for transportation systems. This problem is similar to missing data estimation in contingency tables where the observed data, the table margins, give little information to drive the inference. Here we incorporate other sources of data that are common in transportation studies—seed matrices and trip cost distributions—to develop a novel class of hierarchical Bayesian models that provide better estimators. Moreover, classical solutions from growth factor, gravity, and maximum entropy models are identified as specific estimators under the proposed models. We show, however, that each of these solutions account for a small fraction of the posterior probability mass in the ensemble and so we contend that the uncertainty in the inference should be propagated to later analyses or next-stage models. We devise Markov chain Monte Carlo sampling schemes to obtain more robust estimators and perform other types of inferences. We present a synthetic example and a real-world case study in the city of Warwick, Australia, showcasing the proposed models and highlighting how other sources of data can be incorporated in the model to conduct inference in a principled, nonheuristic way. Technical details, data, and an R package are available as supplementary material online.