Abstract
AbstractAs 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.
Highlights
Cl Fitting differential equations to data—a type of inverse problem—is an essential part of modelling in the sciences and engineering
The main contributions of the article are as follows: as a rigorous Bayesian treatment of motorway traffic flow models is rare in the literature, we empirically explore the sampling challenges this offers
After having given a brief review of motorway traffic flow modelling, we fit the fundamental diagram (FD) directly to flowdensity data, but found that estimating the FD and boundary conditions (BCs) with LWR as the forward model resulted in a superior fit in terms of wave speed
Summary
Cl Fitting differential equations to data—a type of inverse problem—is an essential part of modelling in the sciences and engineering. It allows researchers to model complex systems to be able to understand and predict their behavior. We can find applications in such varied fields as Geophysics (Sambridge, 2014), Hydrogeology (Iglesia et al, 2014), and fluid mechanics (Cotter et al, 2009). This research article was awarded Open Data and Open Materials badges for transparent practices. See the Data Availability Statement for details. *The online version of this article has been updated since original publication. A notice detailing the change has been published
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