A Bayesian Statistical Approach for Inference on Static Origin-Destination Matrices

TL;DR

This paper introduces a Bayesian framework for estimating static origin-destination matrices, explicitly modeling trip configurations as random variables and providing more robust inference methods with uncertainty quantification.

Contribution

It develops a novel Bayesian approach that unifies classical OD estimation methods and introduces new estimators and sampling schemes for improved inference.

Findings

Classical solutions are shown to represent only a small part of the posterior probability.

Proposed models allow for uncertainty propagation in OD matrix inference.

Examples demonstrate the incorporation of additional data sources in a principled manner.

Abstract

We address the problem of static OD matrix estimation from a formal statistical viewpoint. We adopt a novel Bayesian framework to develop a class of models that explicitly cast trip configurations in the study region as random variables. As a consequence, classical solutions from growth factor, gravity, and maximum entropy models are identified to specific estimators under the proposed models. We show that each of these solutions usually account for only a small fraction of the posterior probability mass in the ensemble and we then contend that the uncertainty in the inference should be propagated to later analyses or next-stage models. We also propose alternative, more robust estimators and devise Markov chain Monte Carlo sampling schemes to obtain them and perform other types of inference. We present several examples showcasing the proposed models and approach, and highlight how other sources of data can be incorporated in the model and inference in a principled, non-heuristic way.