Statistical Modelling 7 (2007), 73–89
Mixtures and diagnostic plots in modelling road traffic vehicle headways
Gerard J Cowburn
Durham County Council,
UK
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Malcolm Farrow
School of Mathematics and Statistics,
University of Newcastle upon Tyne,
Newcastle upon Tyne, NE1 7RU,
UK
eMail:
malcolm.farrow@newcastle.ac.uk
Abstract:
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.
Keywords:
diagnostic plots; hidden Markov models; Markov chain Monte Carlo;
mixtures; model checking; road traffic
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