  In this paper we present Poisson mixture approaches for origin-destination
(OD) modeling in transportation analysis. We introduce covariate-based models
which incorporate different transport modeling phases and also allow for direct
probabilistic inference on link traffic based on Bayesian predictions. Emphasis
is placed on the Poisson-inverse Gaussian as an alternative to the
commonly-used Poisson-gamma and Poisson-lognormal models. We present a first
full Bayesian formulation and demonstrate that the Poisson-inverse Gaussian is
particularly suited for OD analysis due to desirable marginal and hierarchical
properties. In addition, the integrated nested Laplace approximation (INLA) is
considered as an alternative to Markov chain Monte Carlo and the two
methodologies are compared under specific modeling assumptions. The case study
is based on 2001 Belgian census data and focuses on a large,
sparsely-distributed OD matrix containing trip information for 308 Flemish
municipalities.
