A Bayesian method for estimating traffic flows based on plate scanning
 Enrique Castillo,
 Pilar Jiménez,
 José María Menéndez,
 María Nogal
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In this paper a special conjugate Bayesian method, for reconstructing and estimating traffic flows, based on αshiftedGamma \( \Upgamma (\theta ,\,\lambda ) \) models \( H(\alpha ,\,\theta ,\,\lambda ) \) is given. If the numbers of users traveling through different routes are assumed to be independent \( H(\alpha ,\,\theta ,\,\lambda) \) variables with common \( \lambda,\) the link, origin–destination (OD) and node flows are also \( H(\alpha ,\,\theta ,\,\lambda ) \) random variables. We assume that the main source of information is plate scanning, which permits us to identify, totally or partially, the vehicle route, OD and link flows by scanning their corresponding plate numbers at an adequately selected subset of links. The reconstruction of the sample flows can be done exactly or approximately, depending on the intensity of the plate scanning sampling procedure. To this end a generalized least squares technique is used together with the conservation laws. A Bayesian approach using special conjugate families is proposed that allows us to estimate different traffic flows, such as route, ODpair, scanned link or counted link flows. A detailed description of how the prior assessment, the sampling, the posterior updating and the obtention of the Bayesian distribution is given. Finally, one example of application is used to illustrate the methods and procedures.
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 Title
 A Bayesian method for estimating traffic flows based on plate scanning
 Journal

Transportation
Volume 40, Issue 1 , pp 173201
 Cover Date
 20130101
 DOI
 10.1007/s1111601294434
 Print ISSN
 00494488
 Online ISSN
 15729435
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 ShiftedGamma distribution
 Conjugate priors
 Prior assessment of hyperparameters
 Origin–destination and link flow estimation
 Industry Sectors
 Authors

 Enrique Castillo ^{(1)}
 Pilar Jiménez ^{(2)}
 José María Menéndez ^{(2)}
 María Nogal ^{(1)}
 Author Affiliations

 1. Department of Applied Mathematics and Computational Sciences, University of Cantabria, 39005, Santander, Spain
 2. Department of Civil Engineering, University of Castilla La Mancha, 13071, Ciudad Real, Spain