MCMC for a hyperbolic Bayesian inverse problem in traffic flow modelling
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As work on hyperbolic Bayesian inverse problems remains rare in the literature, we explore empirically the sampling challenges these offer which have to do with shock formation in the solution of the PDE. Furthermore, we provide a unified statistical model to estimate using motorway data both boundary conditions and fundamental diagram parameters in LWR, a well known motorway traffic flow model. 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. Finally, we highlight how Population Parallel Tempering - a modification of Parallel Tempering - is a scalable method that can increase the mixing speed of the sampler by a factor of 10.
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