Bayesian inference for network-based models with a linear inverse structure

Network-based transport models are used for a host of purposes, from estimation of travel demand through to traffic assignment and traffic flow prediction. Before any such model can be applied in practice we must estimate its parameters and also examine its adequacy. A variety of methods have been developed to do this, but they are typically quite specific to the particular model at hand. In this paper we show that it is possible to develop a unified approach by recognizing that a statistical linear inverse structure arises when attempting to perform inference for any network-based model. This common structure provides the building blocks for the development a coherent theory for Bayesian inference for these models, which has a number of advantages of over more ad hoc methods. While calculation of the Bayesian posterior will typically be intractable, our unified framework allows us to design a generic Markov chain Monte Carlo algorithm for sampling from this distribution in practice. We illustrate the operation of this algorithm on a section of the road network in the English city of Leicester.