  We propose a Bayesian inference approach for static Origin-Destination
(OD)-estimation in large-scale networked transit systems. The approach finds
posterior distribution estimates of the OD-coefficients, which describe the
relative proportions of passengers travelling between origin and destination
locations, via a Hamiltonian Monte Carlo sampling procedure. We suggest two
different inference model formulations: the instantaneous-balance and
average-delay model. We discuss both models' sensitivity to various count
observation properties, and establish that the average-delay model is generally
more robust in determining the coefficient posteriors. The
instantaneous-balance model, however, requires lower resolution count
observations and produces comparably accurate estimates as the average-delay
model, pending that count observations are only moderately interfered by trend
fluctuations or the truncation of the observation window, and sufficient number
of dispersed data records are available. We demonstrate that the Bayesian
posterior distribution estimates provide quantifiable measures of the
estimation uncertainty and prediction quality of the model, whereas the point
estimates obtained from an alternative constrained quadratic programming
optimisation approach only provide the residual errors between the predictions
and observations. Moreover, the Bayesian approach proves more robust in scaling
to high-dimensional underdetermined problems. The Bayesian
instantaneous-balance OD-coefficient posteriors are determined for the New York
City (NYC) subway network, based on several years of entry and exit count
observations recorded at station turnstiles across the network. The
average-delay model proves intractable on the real-world test scenario, given
its computational time complexity and the incompleteness as well as coarseness
of the turnstile records.
