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

Abstract

In this paper, we review both the fundamentals and the expansion of computational Bayesian econometrics and statistics applied to transportation modeling problems in road safety analysis and travel behavior. Whereas for analyzing accident risk in transportation networks there has been a significant increase in the application of hierarchical Bayes methods, in transportation choice modeling, the use of Bayes estimators is rather scarce. We thus provide a general discussion of the benefits of using Bayesian Markov chain Monte Carlo methods to simulate answers to the problems of point and interval estimation and forecasting, including the use of the simulated posterior for building predictive distributions and constructing credible intervals for measures such as the value of time. Although there is the general idea that going Bayesian is just another way of finding an equivalent to frequentist results, in practice Bayes estimators have the potential of outperforming frequentist estimators and, at the same time, may offer more information. Additionally, Bayesian inference is particularly interesting for small samples and weakly identified models.

Keywords:

• Bayesian statistics
• MCMC
• discrete choice
• road safety

Notes

Bayes estimators have properties that are valid for small samples.

Prior knowledge includes building on previous research as well as theoretical constraints, such as parameters having a particular sign.

For small samples, frequentist estimators lose their good statistical properties.

Because of the lack of disaggregate data, traffic exposure is usually defined according to the average annual daily traffic (ADDT) flows. Little work has been focused on the relationships between crashes and other traffic flow characteristics such as vehicle density, level of service, vehicle occupancy, speed distribution, etc. (Lord, Washington, & Ivan, 2005). Few works have considered hourly exposure functions accounting for traffic composition and other temporal variations (we refer to the work of Qin, Ivan, & Ravishanker, 2004).

Spatial dependency of θ _it with respect to other sites — which suggests that sites that are closer to each other are more likely to have common features affecting their accident occurrence.

For instance, if θ ˆ _i is equal to two accidents per year, it means that in five years 10 accidents are expected.

Brownstone and Fang (2009) address the problem of endogeneity, which was absent in the estimator derived by Fang (2008).

Two exceptions are the work of Brownstone and Fang (2009), where the authors perform an out-of-sample check of vehicle choice and utilization forecasts using predictive posteriors, and the credible sets of willingness-to-pay derived in Daziano and Achtnicht (2012).

This widely studied dataset was collected in 1989 by VIA Rail to analyze the demand for a high-speed train in the Toronto-Montréal corridor (Bhat, 1995; Forinash & Koppelman, 1993; Koppelman & Wen, 2000).