Inference for origin–destination matrices: Estimation, prediction and reconstruction

This paper concerns inference about an origin–destination (O–D) matrix from a single observation on a set of network link flows. Two problems in this area have received attention; first, the problem of reconstructing the actual number of O–D trips, and second, estimation of mean O–D trip rates. Little distinction has been drawn between these in the literature: indeed, it has sometimes been implicitly suggested that their a posteriori most probable solutions are identical. We show that this is not the case. An example is provided to demonstrate that the dissimilarity between the solutions to the two problems is potentially unbounded. The relative merits of reconstructed versus estimated mean trip count vectors are discussed with particular reference to their use as predictors of future traffic flows.