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Markov chain Monte Carlo for a hyperbolic Bayesian inverse problem in traffic flow modeling

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Article numbere4
<mark>Journal publication date</mark>31/03/2022
<mark>Journal</mark>Data-Centric Engineering
Number of pages23
Publication StatusPublished
Early online date22/02/22
<mark>Original language</mark>English


As a Bayesian approach to fitting motorway traffic flow models remains rare in the literature, we empirically explore the sampling challenges this approach offers which have to do with the strong correlations and multimodality of the posterior distribution. In particular, we provide a unified statistical model to estimate using motorway data both boundary conditions and fundamental diagram parameters in a motorway traffic flow model due to Lighthill, Whitham, and Richards known as LWR. This allows us to provide a traffic flow density estimation method that is shown to be superior to two methods found in the traffic flow literature. To sample from this challenging posterior distribution, we use a state-of-the-art gradient-free function space sampler augmented with parallel tempering.