Bayesian inference for transportation origin-destination matrices: the Poisson-inverse Gaussian and other Poisson mixtures

Transportation origin-destination analysis is investigated through the use of Poisson mixtures by introducing covariate-based models which incorporate different transport modelling phases and also allow for direct probabilistic inference on link traffic based on Bayesian predictions. Emphasis is placed on the Poisson-inverse Gaussian model as an alternative to the commonly used Poisson-gamma and Poisson-log-normal models. We present a first full Bayesian formulation and demonstrate that the Poisson-inverse Gaussian model is particularly suited for origin-destination analysis because of its desirable marginal and hierarchical properties. In addition, the integrated nested Laplace approximation is considered as an alternative to Markov chain Monte Carlo sampling and the two methodologies are compared under specific modelling assumptions. The case-study is based on 2001 Belgian census data and focuses on a large, sparsely distributed origin-destination matrix containing trip information for 308 Flemish municipalities.