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

Coullon, J; Pokern, Y; (2022) Markov chain Monte Carlo for a hyperbolic Bayesian inverse problem in traffic flow modeling. Data-Centric Engineering , 3 , Article e4. 10.1017/dce.2022.3. Green open access

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Abstract

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.

Type: Article
Title: Markov chain Monte Carlo for a hyperbolic Bayesian inverse problem in traffic flow modeling
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/dce.2022.3
Publisher version: https://doi.org/10.1017/dce.2022.3
Language: English
Additional information: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited
Keywords: Bayesian inverse problem; MCMC; motorway traffic flow; traffic engineering; uncertainty quantification
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL
URI: https://discovery.ucl.ac.uk/id/eprint/10145366
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