A Bayesian semi-parametric model to estimate relationships between crash counts and roadway characteristics
This paper uses a semi-parametric Poisson-gamma model to estimate the relationships between crash counts and various roadway characteristics, including curvature, traffic levels, speed limit and surface width. A Bayesian nonparametric estimation procedure is employed for the model's link function, substantially reducing the risk of a mis-specified model. It is shown via simulation that little is lost in terms of estimation quality if the nonparametric estimation procedure is used when standard parametric assumptions (e.g., linear functional forms) are satisfied, but there is significant gain if the parametric assumptions are violated. It is also shown that imposing appropriate monotonicity constraints on the relationships provides better function estimates. Results suggest that key factors for explaining crash rate variability across roadways are the amount and density of traffic, presence and degree of a horizontal curve, and road classification. Issues related to count forecasting on individual roadway segments and out-of-sample validation measures also are discussed.
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Volume (Year): 44 (2010)
Issue (Month): 5 (June)
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- Smith, M. & Kohn, R., .
"Nonparametric Regression using Bayesian Variable Selection,"
Statistics Working Paper
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- Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
- Dunson, David B., 2005. "Bayesian Semiparametric Isotonic Regression for Count Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 618-627, June.
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- Thomas S. Shively & Thomas W. Sager & Stephen G. Walker, 2009. "A Bayesian approach to non-parametric monotone function estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 159-175.
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