Markov chain Monte Carlo based inverse modeling of traffic flows using GPS data. In large scale deployments of traffic flow models, estimation of the model parameters is a critical but cumbersome task. A poorly calibrated model leads to erroneous estimates in data-poor environments, and limited forecasting ability. In this article we present a method for calibrating flow model parameters for a discretized scalar conservation law using only velocity measurements. The method is based on a Markov Chain Monte Carlo technique, which is used to approximate statistics of the posterior distribution of the model parameters. Numerical experiments highlight the difficulty in estimating jam densities and provide a new approach to improve performance of the sampling through re-parameterization of the model. Supporting source code for the numerical experiments is available for download at url{}.

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