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MCMC for a hyperbolic Bayesian inverse problem in motorway traffic flow

Coullon, Jeremie; (2019) MCMC for a hyperbolic Bayesian inverse problem in motorway traffic flow. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Abstract

We study the LWR model: a hyperbolic conservation law used to model traffic flow on motorways. This is an old model dating back to the 1950s, but has been shown to be robust and is parametrised by the so-called Fundamental Diagram (FD) which provides the relationship between flow and density. We consider the boundary conditions as nuisance parameters to be estimated but neglect the initial conditions as their effect on data is quickly washed out. // The data we use to estimate the parameters in the model is MIDAS data on a section of motorway that does not include any on/off ramps, thus conforming with the nature of the model as a conservation law. Little statistically sound work has been done so far on this inverse problem to estimate the FD parameters as well as the boundary conditions. // We consider two families of FDs, Del Castillo’s FD and the exponential FD – which have 4 and 2 parameters respectively – and perform inference for these along with the boundary conditions. We assume as prior that the boundary conditions follow a log Ornstein Uhlenbeck process which corresponds surprisingly well to practitioners’ prior belief. // We use standard MCMC methods (Gibbs, RWMH, parallel tempering, functional preconditioned RWMH) to sample from the posterior distribution. For some models, the posterior is highly correlated, multimodal and non-Gaussian, so we introduce novel proposals and find that while these are underpinned by clear intuition and show great promise in preliminary studies, they do not seem to appreciably accelerate mixing judging from the studies carried out so far.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: MCMC for a hyperbolic Bayesian inverse problem in motorway traffic flow
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Copyright © The Author 2019. Original content in this thesis is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
URI: https://discovery.ucl.ac.uk/id/eprint/10078714
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