Bayesian Inference for Origin-Destination Matrices of Transport Networks Using the EM Algorithm

Abstract

Information on the origin-destination (OD) matrix of a transport network is a fundamental requirement in much transportation planning. A relatively inexpensive method for updating an OD matrix is to draw inference about the OD matrix based on a single observation of traffic flows on a specific set of network links, where the Bayesian approach is a natural choice for combining the prior knowledge about the OD matrix and the current observation of traffic flows. The existing approaches of Bayesian modeling of OD matrices include using normal approximations to Poisson distributions, which leads to the posterior being intractable even under some simple special cases, and using Markov chain Monte Carlo simulation, which incurs extreme demand of computational efforts. In this article, through the EM algorithm, Bayesian inference is reinvestigated for a transport network for estimating the population means of traffic flows, reconstructing traffic flows, and predicting future traffic flows. It is shown that the resultant estimates have very simple forms with minimal computational costs.

KEY WORDS :

• Bayesian statistical modeling
• Incomplete data analysis
• Multivariate negative binomial distribution
• Multivariate Poisson distribution
• Trip matrix