Data-driven uncertainty quantification in macroscopic traffic flow models

We propose a Bayesian approach for parameter uncertainty quantification in macroscopic traffic flow models from cross-sectional data. We consider both a simple first order model consisting in the mass conservation equation and its second order version including a speed evolution equation. A bias term is introduced and modeled as a Gaussian process to account for the traffic flow models limitations. We validate the results comparing the error in the macroscopic variables (flow, speed, density) for both models, showing that second order models globally perform better in reconstructing traffic quantities of interest.