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Estimating and predicting traffic conditions in arterial networks using probe data has proven to be a substantial challenge. Sparse probe data represent the vast majority of the data available on arterial roads. This paper proposes a probabilistic modeling framework for estimating and predicting arterial travel-time distributions using sparsely observed probe vehicles. We introduce a model based on hydrodynamic traffic theory to learn the density of vehicles on arterial road segments, illustrating the distribution of delay within a road segment. The characterization of this distribution is essentially to use probe vehicles for traffic estimation: Probe vehicles report their location at random locations, and the travel times between location reports must be properly scaled to match the map discretization. A dynamic Bayesian network represents the spatiotemporal dependence on the network and provides a flexible framework to learn traffic dynamics from historical data and to perform real-time estimation with streaming data. The model is evaluated using data from a fleet of 500 probe vehicles in San Francisco, CA, which send Global Positioning System (GPS) data to our server every minute. The numerical experiments analyze the learning and estimation capabilities on a subnetwork with more than 800 links. The sampling rate of the probe vehicles does not provide detailed information about the location where vehicles encountered delay or the reason for any delay (i.e., signal delay, congestion delay, etc.). The model provides an increase in estimation accuracy of 35% when compared with a baseline approach to process probe-vehicle data.