[en] Transportation origin–destination analysis is investigated through the use of Poisson mixtures by introducing covariate-based models which incorporate different transport modelling phases and also allow for direct probabilistic inference on link traffic based on Bayesian predictions. Emphasis is placed on the Poisson–inverse Gaussian model as an alternative to the commonly used Poisson–gamma and Poisson–log-normal models. We present a first full Bayesian formulation and demonstrate that the Poisson–inverse Gaussian model is particularly suited for origin–destination analysis because of its desirable marginal and hierarchical properties. In addition, the integrated nested Laplace approximation is considered as an alternative to Markov chain Monte Carlo sampling and the two methodologies are compared under specific modelling assumptions. The case-study is based on 2001 Belgian census data and focuses on a large, sparsely distributed origin–destination matrix containing trip information for 308 Flemish municipalities.
Research Center/Unit :
Lepur : Centre de Recherche sur la Ville, le Territoire et le Milieu rural - ULiège LEMA - Local Environment Management and Analysis
Disciplines :
Special economic topics (health, labor, transportation...) Civil engineering
Author, co-author :
Perrakis, Konstantinos
Karlis, Dimitris
Cools, Mario ; Université de Liège - ULiège > Département Argenco : Secteur A&U
Janssens, Davy
Language :
English
Title :
Bayesian inference for transportation origin–destination matrices: the Poisson–inverse Gaussian and other Poisson mixtures
Publication date :
2015
Journal title :
Journal of the Royal Statistical Society. Series A, Statistics in Society
Aitkin, A. (1996) A general maximum likelihood analysis of overdispersion in generalized linear models. Statist. Comput., 6, 251-262.
Athreya, K. B. (1986) Another conjugate family for the normal distribution. Statist. Probab. Lett., 4, 61-64.
Boucher, J.-P. and Denuit, M. (2006) Fixed versus random effects in Poisson regression models for claim counts: a case study with motor insurance. Astin Bull., 1, 285-301.
Breslow, N. E. (1984) Extra-Poisson variation in log-linear models. Appl. Statist., 33, 38-44.
Brooks, S. P. and Gelman, A. (1998) General methods for monitoring convergence of iterative simulations. J. Computnl Graph. Statist., 7, 434-455.
Bureau of Public Roads (1964) Traffic Assignment Manual for Application with a Large, High Speed Computer. Washington: US Department of Commerce Bureau of Public Roads.
Carlson, M. (2002) Assessing microdata disclosure risk using the Poisson-inverse Gaussian distribution. Statist. Transn, 5, 901-925.
Chen, J. J. and Ahn, H. (1996) Fitting mixed Poisson regression models using quasi-likelihood methods. Biometr. J., 38, 81-96.
Chib, S. and Greenberg, E. (1995) Understanding the Metropolis-Hastings algorithm. Am. Statistn, 49, 327-335.
Dagpunar, J. (1988) Principles of Random Variate Generation. New York: Oxford University Press.
Dean, C., Lawless, J. F. and Willmot, G. E. (1989) A mixed Poisson-inverse-Gaussian regression model. Can. J. Statist., 17, 171-181.
Fernández, C., Ley, E. and Steel, M. F. J. (2001) Benchmark priors for Bayesian model averaging. J. Econmetr., 100, 381-427.
Font, M., Puig, X. and Ginebra, J. (2013) A Bayesian analysis of frequency count data. J. Statist. Computn Simuln, 83, 229-246.
Gelman, A. (2006) Prior distributions for variance parameters in hierarchical models. Baysn Anal., 1, 515-533.
Gelman, A. and Hill, J. (2006) Data Analysis using Regression and Multilevel/Hierarchical Models, 1st edn. New York: Cambridge University Press.
Gelman, A. and Rubin, D. B. (1992) Inference from iterative simulation using multiple sequences. Statist. Sci., 7, 457-511.
Hazelton, M. L. (2010) Bayesian inference for network-based models with a linear inverse structure. Transprtn Res. B, 44, 674-685.
Holla, M. S. (1967) On a Poisson-inverse Gaussian distribution. Metrika, 11, 115-121.
Jenelius, E., Petersen, T. and Mattsson, L. G. (2006) Importance and exposure in road network vulnerability analysis. Transprtn Res. A, 40, 537-560.
Jorgensen, B. (1982) Statistical Properties of the Generalized Inverse Gaussian Distribution. New York: Springer.
Karlis, D. (2001) A general EM approach for maximum likelihood estimation in mixed Poisson regression models. Statist. Modllng, 1, 305-318.
Lawless, J. F. (1987) Negative binomial and mixed Poisson regression. Can. J. Statist., 15, 209-225.
Lee, Y. and Nelder, J. A. (1996) Hierarchical generalized linear models (with discussion). J. R. Statist. Soc. B, 58, 619-678.
Lee, Y. and Nelder, J. A. (2004) Conditional and marginal models: another view. Statist. Sci., 19, 219-228.
Martins, T. G. and Rue, H. (2013) Extending INLA to a class of near-Gaussian latent models. Preprint arXiv:1210.1434v2.
Medina, A., Taft, N., Salamatian, K., Bhattacharyya, S. and Diot, C.(2002) Traffic matrix estimation. In Proc. Conf. Applications, Technologies, Architectures and Protocols for Computer Communications.New York: Association for Computing Machinery Press.
Meng, X.-L. (1994) Posterior predictive p-values. Ann. Statist., 22, 1142-1160.
Nikoloulopoulos, A. K. and Karlis, D. (2008) On modeling count data: a comparison of some well-known discrete distributions. J. Statist. Computn Simuln, 78, 437-457.
Ntzoufras, I. (2009) Bayesian Modeling using WinBUGS, 1st edn. New York: Wiley.
Odoki, J. B., Kerali, H. R. and Santorini, F. (2001) An integrated model for quantifying accessibility-benefits in developing countries. Transportn Res. A, 35, 601-623.
Ortúzar, J. de Dios and Willumsen, L. G. (2001) Modelling Transport, 3rd edn. Chichester: Wiley.
Perrakis, K., Cools, M., Karlis, D., Janssens, D., Kochan, B., Bellemans, T. and Wets, G. (2012a) Quantifying input-uncertainty in traffic assignment models. In Proc. 91st A.Meet.Transportation Research Board. Washington DC: Transportation Research Board.
Perrakis, K., Karlis, D., Cools, M., Janssens, D., Vanhoof, K. and Wets, G. (2012b) A Bayesian approach for modeling origin-destination matrices. Transportn Res. A, 46, 200-212.
Puig, X., Ginebra, J. and Perez-Casany, M. (2009) Extended truncated inverse-Gaussian Poisson model. Statist. Modllng, 9, 151-171.
R Core Team (2013) R: a Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing.
Rue, H., Martino, S. and Chopin, N. (2009) Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (with discussion). J. R. Statist. Soc. B, 71, 319-392.
Shaban, S. A. (1988) Poisson-lognormal distributions. In Log-normal Distributions: Theory and Applications (eds E. L. Crow and K. Shimizu ), pp. 195-210. New York: Dekker.
Sohn, K. and Kim, D. (2010) Zonal centrality measures and the neighborhood effect. Transprtn Res. A, 44, 733-744.
Spiegelhalter, D., Thomas, A., Best, N. and Lunn, D. (2003) WinBUGS User Manual, Version 1.4. Cambridge: Medical Research Council Biostatistics Unit. (Available from http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/manual14.pdf.)
Tebaldi, C. and West, M. (1998) Bayesian inference on network traffic using link count data (with discussion). J. Am. Statist. Ass., 93, 557-576.
Thomas, R. (1991) Traffic Assignment Techniques. Aldershot: Avebury Technical.
Wardrop, J. (1952) Some theoretical aspects of road traffic research. Proc. Inst. Civ. Engrs II, 1, 352-362.
West, M. (1994) Statistical inference for gravity models in transportation flow forecasting. Discussion Paper 94-40. Institute of Statistics and Decision Sciences, Duke University, Durham.
Willmot, G. E. (1987) The Poisson-inverse Gaussian distribution as an alternative to the negative binomial. Scand. Act. J., 3-4, 113-127.
Yao, E. and Morikawa, T. (2005) A study of an integrated intercity travel demand model. Transprtn Res. A, 39, 367-381.
Zellner, A. (1986) On assessing prior distributions and Bayesian regression analysis with g-prior distributions. In Bayesian Inference and Decision Techniques: Essays in Honour of Bruno de Finetti (eds P. Goel and A. Zellner ), pp. 233-243. Amsterdam: North-Holland.