  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.
