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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.The average-delay model is generally more robust in determining accurate and precise coefficient posteriors across various combinations of observation properties. The instantaneous-balance model, however, requires lower resolution count observations and produces estimates comparable to the average-delay model, pending that certain count observation properties are met. We demonstrate that the Bayesian posterior distribution estimates provide quantifiable measures of the estimation uncertainty and prediction quality of the model. Moreover, the Bayesian approach is at least as accurate as existing optimisation approaches and proves robust in scaling to high-dimensional underdetermined problems without suffering from the curse of dimensionality. The Bayesian instantaneous-balance model is applied to the New York City subway network, with several years of entry and exit count observations recorded at several hundred station turnstiles across the network. The posterior distribution estimates provide intuitive demand patterns and are projected to be more valuable than point estimates, since they allow for robust transport network designs that account for the uncertainty of network parameters.
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