A Bayesian Approach for Modeling Origin-Destination Matrices

The majority of Origin Destination (OD) matrix estimation methods focus on situations where weak or partial information, derived from sample travel surveys, is available. Information derived from travel census studies, in contrast, covers the entire population of a specific study area of interest. In such cases where reliable historical data exist, statistical methodology may serve as a flexible alternative to traditional travel demand models by incorporating estimation of trip-generation, trip-attraction and trip-distribution in one model. In this research, a statistical Bayesian approach on OD matrix estimation is presented, where modeling of OD flows, derived from census data, is related only to a set of general explanatory variables. The assumptions of a Poisson model and of a Negative-Binomial model are investigated on a realistic application area concerning the region of Flanders on the level of municipalities. Problems related to the absence of closed-form expressions are bypassed with the use of a Markov Chain Monte Carlo algorithm, known as the Metropolis-Hastings algorithm. Additionally, a strategy is proposed in order to obtain predictions from the hierarchical, Poisson-Gamma structure of the Negative-Binomial model conditional on the posterior expectations of the mixing parameters. In general, Bayesian methodology reduces the overall uncertainty of the estimates by delivering posterior distributions for the parameters of scientific interest as well as predictive distributions for future OD flows. Predictive goodness-of-fit tests suggest a good fit to the data and overall results indicate that the approach is applicable on large networks, with relatively low computational and explanatory data-gathering costs.