Computational Bayesian statistics in transportation modeling: from road safety analysis to discrete choice

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.