Computational Bayesian Statistics in Transportation Modeling: From Road Safety Analysis to Discrete Choice

Transport Reviews

Volumn 33, Issue 5, 2013, Pages 570-592

  Daziano, Ricardo A ^a   Miranda Moreno, Luis ^b   Heydari, Shahram ^b  

^a School of Operations Research and Industrial Engineering   (United States)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

Bayesian statistics; discrete choice; MCMC; road safety

Indexed keywords

BAYESIAN ANALYSIS; DISCRETE CHOICE ANALYSIS; ECONOMETRICS; MARKOV CHAIN; MATHEMATICAL ANALYSIS; MONTE CARLO ANALYSIS; NUMERICAL MODEL; SAFETY; TRANSPORTATION ECONOMICS; TRANSPORTATION MODE; TRAVEL BEHAVIOR;

EID: 84884353934     PISSN: 01441647     EISSN: 14645327     Source Type: Journal    
DOI: 10.1080/01441647.2013.829890     Document Type: Review

References (80)

1. Abbess, C., Jarrett, D. F. and Wright, C. C. 1981. Accidents at blackspots: Estimating the effectiveness of remedial treatment, with special reference to the regression-to-mean effect. Traffic Engineering and Control, 22 (10): 535 - 542.
2. Aguero-Valverde, J. and Jovanis, P. P. 2009. Bayesian multivariate Poisson Log-Normal models for crash severity modeling and site ranking. Transportation Research Record, 2136: 82 - 91. (doi:10.3141/2136-10)
3. Aguirregabiria, V. and Mira, P. 2010. Dynamic discrete choice structural models: A survey. Journal of Econometrics, 156 (1): 38 - 67. (doi:10.1016/j.jeconom.2009.09.007)
4. Albert, J. and Chib, S. 1993. Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88: 669 - 679. (doi:10.1080/01621459.1993.10476321)
5. Aul, N., & Davis, G. (2006). Use of propensity score matching method and hybrid Bayesian method to estimate crash modification factors of signal installation. Transportation Research Record: Journal of the Transportation Research Board, 1950, 17-23.
6. Bhat, C. R. 1995. A heteroscedastic extreme-value model of intercity mode choice. Transportation Research B, 29 (6): 471 - 483. (doi:10.1016/0191-2615(95)00015-6)
7. Bolduc, D., Fortin, B. and Gordon, S. 1997. Multinomial probit estimation of spatially interdependent choices: An empirical comparison of two new techniques. International Regional Science Review, 20: 77 - 101. (doi:10.1177/016001769702000105)
8. Brijs, T., Karlis, D., Van den Bossche, F. and Wets, G. 2007. A Bayesian model for ranking hazardous road sites. Journal of the Royal Statistical Society Series A, 170: 1 - 17.
9. Brownstone, D. 2001. " Discrete choice modelling for transportation ". In Travel behaviour research: The leading edge, Edited by: Hensher, D. A. 97 - 124. Oxford: Pergamon Press.
10. Brownstone, D., & Fang, H. (2009). A vehicle ownership and utilization choice model with endogenous residential density. Working paper, Department of Economics, University of California, Irvine.
11. Cheng, L., Geedipally, S. R. and Lord, D. 2012. Examining the Poisson-Weibull generalized linear model for analyzing crash data. Safety Science, 54: 38 - 42. (doi:10.1016/j.ssci.2012.11.002)
12. Chib, S., Greenberg, E., & Chen, Y. (1998). MCMC methods for fitting and comparing multinomial response models. Econometrics 9802001, EconWPA.
13. Damien, P. and Kockelman, K. M. 2010. Preface to special issue on Bayesian methods. Transportation Research Part B, 44 (5): 631 - 632. (doi:10.1016/j.trb.2010.03.005)
14. Daziano, R. A., & Achtnicht, M. (2012). Accounting for uncertainty in willingness to pay for environmental benefits. Working Paper, School of Civil and Environmental Engineering, Cornell University, Mannheim, Germany.
15. Daziano, R. A., & Bolduc, D. (2013). Incorporating pro-environmental preferences toward green automobile technologies through a Bayesian Hybrid Choice Model. Transportmetrica A: Transport Science, 9(1), 74-106.
16. Edwards, Y. and Allenby, G. 2003. Multivariate analysis of multiple response data. Journal of Marketing Research, 40: 321 - 334. (doi:10.1509/jmkr.40.3.321.19233)
17. El-Basyouny, K., & Sayed, T. (2010). A full Bayes approach to before-after safety evaluation with matched comparisons: A case study of stop-sign in-fill program. Transportation Research Record: Journal of the Transportation Research Board, 2148, 1-8.
18. El-Basyouny, K. and Sayed, T. 2012. Depth-based hotspot identification and multivariate ranking using the full Bayes approach. Accident Analysis and Prevention, 50: 1082 - 1089. (doi:10.1016/j.aap.2012.08.019)
19. Elvik, R. (2009). The non-linearity of risk and the promotion of environmentally sustainable transport. Accident Analysis and Prevention, 41(4), 849-855.
20. Fang, A. 2008. A discrete-continuous model of households' vehicle choice and usage, with an application to the effects of residential density. Transportation Research Part B, 42 (9): 736 - 758. (doi:10.1016/j.trb.2008.01.004)
21. Forinash, C. V. and Koppelman, F. S. 1993. Application and interpretation of nested logit models of intercity mode choice. Transportation Research Record, 1413: 98 - 106.
22. Frühwirth-Schnatter, S. and Frühwirth, R. 2010. " Data augmentation and MCMC for binary and multinomial logit models ". In Statistical modelling and regression structures, Edited by: Kneib, Thomas and Tutz, Gerhard. 111 - 132. Heidelberg: Physica-Verlag.
23. Gelfand, A. E. and Smith, A. F. M. 1990. Sampling-Based approaches to calculating marginal densities. Journal of the American Statistical Association, 85: 398 - 409. (doi:10.1080/01621459.1990.10476213)
24. Geweke, J. 1991. " Efficient simulation from the multivariate normal and Student-t distributions subject to linear constraints ". In Computer science and statistics: Proceedings of the twenty-third symposium on the interface, Edited by: Keramidas, E. M. 571 - 578. Fairfax: Interface Foundation of North America.
25. Geweke, J. F., Keane, M. P. and Runkle, D. E. 1997. Statistical inference in the multinomial multiperiod probit model. Journal of Econometrics, 80: 125 - 165. (doi:10.1016/S0304-4076(97)00005-5)
26. Gourieroux, C., & Monfort, A. (1995). Statistics and econometric models. New York, NY: Cambridge University Press.
27. Greenberg, E. (2007). Introduction to Bayesian Econometrics. New York, NY: Cambridge University Press.
28. Greene, W. H. and Hensher, D. 2003. A latent class model for discrete choice analysis: Contrasts with mixed logit. Transportation Research Part B, 37: 681 - 698. (doi:10.1016/S0191-2615(02)00046-2)
29. Hauer, E. 1997. Observational before-after studies in road safety: Estimating the effect of highway and traffic engineering measures on road safety, Oxford: Elsevier Science Ltd.
30. Hauer, E. and Persaud, B. N. 1987. How to estimate the safety of rail-highway grade crossings and the safety effects of warning devices. Transportation Research Record, 1114: 131 - 140.
31. Hensher, D. A. and Greene, W. H. 2003. The mixed logit model: The state of practice. Transportation, 30 (2): 133 - 176. (doi:10.1023/A:1022558715350)
32. Heydari, S., Miranda-Moreno, L. F., & Amador, L. (2013). Does prior specification matter in hotspot identification and before-after studies in road safety? Transportation Research Record: Journal of the Transportation Research Board (In press).
33. Heydecker, B. G. and Wu, J. 2001. Identification of road sites for accident remedial work by Bayesian statistical methods: An example of uncertain inference. Advances in Engineering Software, 32: 859 - 869. (doi:10.1016/S0965-9978(01)00037-0)
34. Higle, J. L. and Witkowski, J. M. 1988. Bayesian identification of hazardous sites. Transportation Research Record, 1185: 24 - 35.
35. Huang, H. and Abdel-Aty, M. 2010. Multilevel data and Bayesian analysis in traffic safety. Accident Analysis & Prevention, 42 (6): 1556 - 1565. (doi:10.1016/j.aap.2010.03.013)
36. Imai, K. and Van Dyk, D. A. 2005. A Bayesian analysis of the multinomial probit model using marhinal data augmentation. Journal of Econometrics, 124: 311 - 334. (doi:10.1016/j.jeconom.2004.02.002)
37. Imai, S., Jain, N. and Ching, A. 2009. Bayesian estimation of dynamic discrete choice models. Econometrica, 77 (6): 1865 - 1899. (doi:10.3982/ECTA5658)
38. Kim, Y., Kim, T. Y. and Heo, E. 2003. Bayesian estimation of multinomial probit models of work trip choice. Transportation, 30: 351 - 365. (doi:10.1023/A:1023914313215)
39. Koop, G. and Poirier, D. J. 1993. Bayesian analysis of logit models using natural conjugate priors. Journal of Econometrics, 56: 323 - 340. (doi:10.1016/0304-4076(93)90124-N)
40. Koppelman, F. S. and Wen, C-H. 2000. The paired combinatorial logit model: Properties, estimation and application. Transportation Research B, 34: 75 - 89. (doi:10.1016/S0191-2615(99)00012-0)
41. KPMG Peat Marwick, & Koppelman, F. S. (1990). Proposal for Analysis of the Market Demand for High Speed Rail in the Quebec/Ontario Corridor. Submitted to Ontario/Quebec Rapid Train Task Force.
42. Krinsky, I. and Robb, A. L. 1986. On approximating the statistical properties of elasticities. Review of Economic and Statistics, 68: 715 - 719. (doi:10.2307/1924536)
43. Lahiri, K. and Gao, J. 2002. Bayesian analysis of nested logit model by Markov Chain Monte Carlo. Journal of Econometrics, 111: 103 - 133. (doi:10.1016/S0304-4076(02)00125-2)
44. Lan, B. and Persaud, B. 2011. Fully Bayesian approach to investigate and evaluate ranking criteria for black spot identification. Transportation Research Record, 2237: 117 - 125. (doi:10.3141/2237-13)
45. Lan, B., Persaud, B., Lyon, C., & Bhim, R. (2009). Validation of a full Bayes methodology for observational before-after road safety studies and application to evaluation of rural signal conversions. Accidents Analysis and Prevention, 41(3), 574-580.
46. Lancaster, T. (2004). Introduction to Modern Bayesian Econometrics. Malden MA: Blkackwell.
47. Lemp, D., Kockelman, K. M. and Damien, P. 2010. The continuous cross-nested logit model: Formulation and application for departure time choice. Transportation Research Part B, 44 (5): 646 - 661. (doi:10.1016/j.trb.2010.03.001)
48. Li, W., Carriquiry, A., Pawlovich, M., & Welch, T. (2008). The choice of statistical models in road safety countermeasures effectiveness studies in Iowa. Accident Analysis and Prevention, 40(4), 1531-1542.
49. Lord, D., & Miranda-Moreno, L. F. (2008). Effects of the low sample mean values and the small sample size on the estimation of the fixed dispersion parameter of Poisson-gamma models: A Bayesian perspective. Safety Science, 46, 751-770.
50. Lord, D., Washington, S. P. and Ivan, J. N. 2005. Poisson, Poisson-Gamma and zero inflated regression models of motor vehicle crashes: Balancing statistical fit and theory. Accident Analysis and Prevention, 37 (1): 35 - 46. (doi:10.1016/j.aap.2004.02.004)
51. McCulloch, R. R., Polson, N. G. and Rossi, P. E. 2000. Bayesian analysis of the multinomial probit model with fully identified parameters. Journal of Econometrics, 99: 173 - 193. (doi:10.1016/S0304-4076(00)00034-8)
52. Miaou, S. P. and Lord, D. 2003. Modeling traffic crash-flow relationships for intersections: Dispersion parameter, functional form, and Bayes versus Empirical Bayes. Transportation Research Record, 1840: 31 - 40. (doi:10.3141/1840-04)
53. Miaou, S. P. and Song, J. J. 2005. Bayesian ranking of sites for engineering safety improvement: Decision parameter, treatability concept, statistical criterion and spatial dependence. Accident Analysis and Prevention, 37: 699 - 720. (doi:10.1016/j.aap.2005.03.012)
54. Miranda-Moreno, L. F., Fu, L., Saccomano, F. and Labbe, A. 2005. Alternative risk models for ranking locations for safety improvement. Transportation Research Record, 1908: 1 - 8. (doi:10.3141/1908-01)
55. Miranda-Moreno, L. F., Heydari, S., Lord, D., & Fu, L. (2013). Bayesian road safety analysis: Incorporation of past evidence and effect of hyper-prior choice. Journal of Safety Research, 46, 31-40.
56. Miranda-Moreno, L. F., Labbe, A. and Fu, L. 2007. Multiple Bayesian testing procedures for selecting hazardous sites. Accident Analysis and Prevention, 39: 1192 - 1201. (doi:10.1016/j.aap.2007.03.008)
57. Nobile, A. 2000. Bayesian multinomial probit models with a normalization constraint. Journal of Econometrics, 99: 335 - 345. (doi:10.1016/S0304-4076(00)00035-X)
58. Park, E. S., Park, J., & Lomax, T. J. (2010). A fully Bayesian multivariate approach to before-after safety evaluation. Accident Analysis and Prevention, 42(4), 1118-1127.
59. Pawlovich, M. D., Li, W., Carriquiry, A., & Welch, T. (2006). Iowa's experience with road diet measures: Use of Bayesian approach to assess impacts on crash frequencies and crash rates. Transportation Research Record: Journal of the Transportation Research Board, 1953, 163-171.
60. Persaud, B., Lan, B., Lyon, C., & Bhim, R. (2010). Comparison of empirical Bayes and full Bayes approaches for before-after road safety evaluations. Accident Analysis and Prevention, 42, 38-43.
61. Persaud, B., Lyon, C. and Nguyen, T. 1999. Empirical Bayes procedure for ranking sites for safety investigation by potential for safety improvement. Transportation Research Record, 1665: 7 - 12. (doi:10.3141/1665-02)
62. Poirier, D. J. 1996. A Bayesian analysis of nested Logit models. Journal of Econometrics, 75: 163 - 181. (doi:10.1016/0304-4076(95)01775-5)
63. Qin, X., Ivan, J. N. and Ravishanker, N. 2004. Selecting exposure measures in crash rate prediction for two-lane highway segments. Accident Analysis and Prevention, 36 (2): 183 - 191. (doi:10.1016/S0001-4575(02)00148-3)
64. Rao, J. N. 2003. Small area estimation, New York, NY: Wiley.
65. Sándor, Z. and Wedel, M. 2005. Heterogeneous conjoint choice designs. Journal of Marketing Research, 42: 210 - 218. (doi:10.1509/jmkr.42.2.210.62285)
66. Savage, L. J. 1954. The foundations of statistics, New York, NY: Wiley.
67. Scarpa, R., Thiene, M., & Train, K. (2008). Utility in willingness to pay space: A tool to address confounding random scale effects in destination choice to the Alps. American Journal of Agricultural Economics, 90(4), 994-1010.
68. Schluter, P. J., Deely, J. J. and Nicholson, A. J. 1997. Ranking and selecting motor vehicle accident sites by using a hierarchical Bayesian model. The Statistician, 46 (3): 293 - 316.
69. Schultz, G. G., Thurgood, D. J., Olsen, A. N., & Reese, C. S. (2011). Analyzing Raised Median Safety Impacts using Bayesian Methods. Transportation Research Record: Journal of the Transportation Research Board, 2223, 96-103.
70. Scott, S. L. (2011). Data augmentation, frequentist estimation, and the Bayesian analysis of multinomial logit models. Statistical Papers, 52(1), 87-109.
71. Shen, W. and Louis, T. A. 2000. Triple-goal estimates for disease mapping. Statistics in Medicine, 19: 2295 - 2308. (doi:10.1002/1097-0258(20000915/30)19:17/18<2295::AID-SIM570>3.0.CO;2-Q)
72. Sillano, M., & de Ortúzar, J. D. (2005). Willingness-to-pay estimation with mixed logit models: some new evidence. Environment and Planning A, 37(3), 525-550.
73. Song, J. J., Ghosh, M., Miaou, S. and Mallick, B. 2006. Bayesian multivariate spatial models for roadway traffic crash mapping. Journal of Multivariate Analysis, 97: 246 - 273. (doi:10.1016/j.jmva.2005.03.007)
74. Sonnier, G., Ainslie, A. and Otter, T. 2007. Heterogeneity distributions of willingness-to-pay in choice models. Quantitative Marketing and Economics, 5: 313 - 331. (doi:10.1007/s11129-007-9024-6)
75. Train, K. 2009. Discrete choice methods with simulations, New York, NY: Cambridge University Press.
76. Tunaru, R. 2002. Hierarchical Bayesian models for multiple count data. Austrian Journal of Statistics, 31 (3): 221 - 229.
77. Washington, S., Congdon, P., Karlaftis, M. and Mannering, F. 2009. The Bayesian multinomial logit model: Theory and route choice example. Transportation Research Record: Journal of the Transportation Research Board, 2136: 28 - 36. (doi:10.3141/2136-04)
78. Washington, S., Ravulaparthy, S., Rose, J., Hensher, D. and Pendyala, R. 2012. Bayesian imputation of non-chosen attribute values in revealed preference surveys. Journal of Advanced Transportation, doi:10.1002/atr.201
79. Yanmaz-Tuzel, O., & Ozbay, K. (2010). A comparative full Bayesian before-and-after analysis and application to urban road safety countermeasures in New Jersey. Accident Analysis and Prevention, 42(6), 2099-2107.
80. Zou, Y., Zhang, Y. and Lord, D. 2012. Application of finite mixture of negative binomial regression models with varying weight parameters for vehicle crash data analysis. Accident Analysis & Prevention, 50: 1042 - 1051. (doi:10.1016/j.aap.2012.08.004)