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Title: MCMC for a hyperbolic Bayesian inverse problem in motorway traffic flow
Author: Coullon, Jeremie
ISNI:       0000 0004 7970 7147
Awarding Body: UCL (University College London)
Current Institution: University College London (University of London)
Date of Award: 2019
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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.
Supervisor: Buldakov, E. ; Pokern, Y. ; Heydecker, B. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available