MCMC for a hyperbolic Bayesian inverse problem in traffic flow modelling

TL;DR

This paper applies MCMC methods to a Bayesian inverse problem in traffic flow modeling, addressing sampling challenges due to complex posterior distributions and proposing a superior density estimation approach.

Contribution

It introduces a unified Bayesian model for traffic parameters and demonstrates an effective sampling method using gradient-free MCMC with parallel tempering.

Findings

The proposed density estimation outperforms existing methods.

Gradient-free MCMC effectively samples multi-modal posteriors.

Empirical analysis highlights sampling challenges in traffic flow models.

Abstract

As a Bayesian approach to fitting motorway traffic flow models remains rare in the literature, we explore empirically the sampling challenges this approach offers which have to do with the strong correlations and multi-modality 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 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. To sample from this challenging posterior distribution we use a state-of-the-art gradient-free function space sampler augmented with parallel tempering.