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Mixtures and diagnostic plots in modelling road traffic vehicle headways

Gerard J Cowburn, Durham County Council, UK.

Malcolm Farrow

M. Farrow, School of Mathematics and Statistics, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, U.K. E-mail: malcolm.farrow{at}newcastle.ac.uk

We consider Bayesian modelling of the inter-arrival times of vehicles on a road. We give particular attention to model checking and propose diagnostic plots to assess whether the model captures features observed in the data. Models for such processes are important in predicting the behaviour of road junctions. Two-component mixtures have often been used, with a variety of distributions for the components and non-Bayesian methods for fitting. The components are often regarded as representing ‘free flowing’ and ‘congested’ vehicles. We propose a gamma-exponential mixture and compare this with some other models. To allow for the serial dependence of headways, we consider the use of a hidden Markov chain for the mixture component allocation.

Key Words: diagnostic plots • hidden Markov models • Markov chain Monte Carlo • mixtures • model checking • road traffic

Statistical Modelling, Vol. 7, No. 1, 73-89 (2007)
DOI: 10.1177/1471082X0600700105


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