Statistical inference for time varying origin–destination matrices

We consider the problem of estimating a sequence of origin–destination matrices from link count data collected on a daily basis. We recommend a parsimonious parameterization for the time varying matrices so as to permit application of standard statistical estimation theory. A number of examples of suitably parameterized matrices are provided. We propose a multivariate normal model for the link counts, based on an underlying overdispersed Poisson process. While likelihood based inference is feasible given information from sufficiently many network links, we focus on Bayesian methods of estimation because of their ability to incorporate prior information in a natural manner. We derive the Bayesian posterior distribution, but note that its normalizing constant is not available in closed form. A Markov chain Monte Carlo algorithm for generating posterior samples is therefore developed. From this we can obtain point estimates, and corresponding measures of precision, for parameters of the origin–destination matrix. The methodology is illustrated by an example involving OD matrix estimation for a section of the road network in the English city of Leicester.