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

TL;DR

This paper introduces Bayesian Poisson mixture models, especially the Poisson-inverse Gaussian, for transportation OD matrix analysis, providing probabilistic inference and comparing computational methods using Belgian census data.

Contribution

It presents the first full Bayesian formulation of Poisson-inverse Gaussian models for OD matrices and compares INLA with MCMC methods for inference.

Findings

Poisson-inverse Gaussian model shows desirable properties for OD analysis.

INLA provides a computationally efficient alternative to MCMC.

Model applied successfully to Belgian census data with 308 municipalities.

Abstract

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.