Modeling Travel Demand in Portland, Oregon
An important problem in transportation planning is the modeling of patterns of trip-making—especially trips from home (origin) to work (destination) within a fixed geographic area. The standard tool used to study such OD flows is the so-called “gravity model”, a Poisson log-linear regression model for studying the number of trips from origins within one element of a fixed partition area (traffic analysis zone, for example) to destinations within another.
We present an alternative: a gridless Bayesian hierarchical Poisson/gamma random field model, allowing us to incorporate spatial correlation explicitly. The models are fitted to a subset of data from the 1994/95 METRO survey of Portland, Oregon, and are internally validated on a reserved portion of the survey data. Bayesian posterior probability distributions are calculated using a Markov chain Monte Carlo integration scheme based on a novel method for simulating samples from gamma random fields.
Some key wordsBayesian mixture models gamma process Markov chain Monte Carlo simulation
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- Abramowitz, M. and Stegun, I. A., eds., (1964), Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, volume 55 of Applied Mathematics Series, Washington, D.C.: National Bureau of Standards.Google Scholar
- Ben-Akiva, M. and Watanatada, T., (1981), “Application of a Continuous Spatial Choice Logit Model,” in Structural Analysis of Discrete Data with Econometric Applications (eds: C. F. Manski and D. McFadden), 320–343, Cambridge, Mass.: MIT Press.Google Scholar
- Best, N. G., Cowles, M. K., and Vines, S. K., (1995), Convergence diagnosis and output analysis software for Gibbs sampling output,Version 0.3, Cambridge, UK: MRC Biostatistics Unit.Google Scholar
- Casey, H. J., (1955), “Applications to traffic engineering of the law of retail gravitation,” Traffic Quarterly, 100, 23–35.Google Scholar
- Cressie, N. A. C., (1993), Statistics for Spatial Data, New York, NY, USA: John Wiley & Sons.Google Scholar
- Escobar, M. D. and West, M., (1998), “Computing nonparametric hierarchical models,” in Practical Nonparametric and Semiparametric Bayesian Statistics (eds: Dey, D. and Müller, P. and Sinha, D.), New York: Springer-Verlag.Google Scholar
- Gilks, W. R., Richardson, S., and Spiegelhalter, D. J., eds., (1996), Markov Chain Monte Carlo in Practice, New York, NY, USA: Chapman & Hall.Google Scholar
- Ickstadt, K. and Wolpert, R. L., (1997), “Multiresolution Assessment of Forest Inhomogeneity,” in Case Studies in Bayesian Statistics,Volume III (eds: C. Gatsonis, J. S. Hodges, R. E. Kass, R. E. McCulloch, P. Rossi, and N. D. Singpurwalla), volume 121 of Lecture Notes in Statistics, 371–386, New York: Springer-Verlag.Google Scholar
- MacEachern, S. (1998). Computations for Mixture of Dirichlet Process models, in Practical Nonparametric and Semiparametric Bayesian Statistics (eds: Dey, D. and Müller, P. and Sinha, D.), New York: Springer-Verlag.Google Scholar
- Wolpert, R. L. and Ickstadt, K., (1998a), “Poisson/gamma random field models for spatial statistics,” Biometrika, to appear.Google Scholar
- Wolpert, R.L. and Ickstadt, K., (1998b), “Simulation of Lévy Random Fields,” in Practical Nonparametric and Semiparametric Bayesian Statistics (eds: Dey, D. and Müller, P. and Sinha, D.), New York: Springer-Verlag.Google Scholar