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.