A Bayesian approach for modeling origin-destination matrices

Abstract

The Origin Destination (OD) matrix estimation problem is a crucial part of transportation analysis. In this research, a statistical Bayesian approach on OD matrix estimation is presented, where modeling of OD flows is related only to a set of general explanatory variables. The assumptions of a Poisson model and of a Poisson-Gamma mixture model are investigated on a realistic application area concerning the region of Flanders on the level of cities. 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 Poisson-Gamma 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. Results indicate that the approach is applicable on large networks, with relatively low computational and data-gathering costs. Moreover, the methods presented in this study can be naturally extended in order to incorporate different sources of potential uncertainty.