This thesis brings a collection of novel models and methods that result from a new look at practical problems in transportation through the prism of newly available sensor data. There are four main contributions: First, we design a generative probabilistic graphical model to describe multivariate continuous densities such as observed traffic patterns. The model implements a multivariate normal distribution with covariance constrained in a natural way, using a number of parameters that is only linear (as opposed to quadratic) in the dimensionality of the data. This means that learning these models requires less data. The primary use for such a model is to support inferences, for instance, of data missing due to sensor malfunctions.

Second, we build a model of traffic flow inspired by macroscopic flow models. Unlike traditional such models, our model deals with uncertainty of measurement and unobservability of certain important quantities and incorporates on-the-fly observations more easily. Because the model does not admit efficient exact inference, we develop a particle filter. The model delivers better medium- and long- term predictions than general-purpose time series models. Moreover, having a predictive distribution of traffic state enables the application of powerful decision-making machinery to the traffic domain.

Third, two new optimization algorithms for the common task of vehicle routing are designed, using the traffic flow model as their probabilistic underpinning. Their benefits include suitability to highly volatile environments and the fact that optimization criteria other than the classical minimal expected time are easily incorporated. Finally, we present a new method for detecting accidents and other adverse events. Data collected from highways enables us to bring supervised learning approaches to incident detection. We show that a support vector machine learner can outperform manually calibrated solutions. A major hurdle to performance of supervised learners is the quality of data which contains systematic biases varying from site to site. We build a dynamic Bayesian network framework that learns and rectifies these biases, leading to improved supervised detector performance with little need for manually tagged data. The realignment method applies generally to virtually all forms of labeled sequential data.