Markov models for Bayesian analysis about transit route origin–destination matrices

The key factor that complicates statistical inference for an origin–destination (O–D) matrix is that the problem per se is usually highly underspecified, with a large number of unknown entries but many fewer observations available for the estimation. In this paper, we investigate statistical inference for a transit route O–D matrix using on–off counts of passengers. A Markov chain model is incorporated to capture the relationships between the entries of the transit route matrix, and to reduce the total number of unknown parameters. A Bayesian analysis is then performed to draw inference about the unknown parameters of the Markov model. Unlike many existing methods that rely on iterative algorithms, this new approach leads to a closed-form solution and is computationally more efficient. The relationship between this method and the maximum entropy approach is also investigated.