MCMC for a hyperbolic Bayesian inverse problem in motorway traffic flow

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

Urban Informatics

This open access book is the first to systematically introduce the principles of urban informatics and its application to every aspect of the city that involves its functioning, control, management, and future planning. It introduces new models and tools being developed to understand and implement these technologies that enable cities to function more efficiently – to become ‘smart’ and ‘sustainable’. The smart city has quickly emerged as computers have become ever smaller to the point where they can be embedded into the very fabric of the city, as well as being central to new ways in which the population can communicate and act. When cities are wired in this way, they have the potential to become sentient and responsive, generating massive streams of ‘big’ data in real time as well as providing immense opportunities for extracting new forms of urban data through crowdsourcing. This book offers a comprehensive review of the methods that form the core of urban informatics from various kinds of urban remote sensing to new approaches to machine learning and statistical modelling. It provides a detailed technical introduction to the wide array of tools information scientists need to develop the key urban analytics that are fundamental to learning about the smart city, and it outlines ways in which these tools can be used to inform design and policy so that cities can become more efficient with a greater concern for environment and equity

Urban Informatics

This open access book is the first to systematically introduce the principles of urban informatics and its application to every aspect of the city that involves its functioning, control, management, and future planning. It introduces new models and tools being developed to understand and implement these technologies that enable cities to function more efficiently – to become ‘smart’ and ‘sustainable’. The smart city has quickly emerged as computers have become ever smaller to the point where they can be embedded into the very fabric of the city, as well as being central to new ways in which the population can communicate and act. When cities are wired in this way, they have the potential to become sentient and responsive, generating massive streams of ‘big’ data in real time as well as providing immense opportunities for extracting new forms of urban data through crowdsourcing. This book offers a comprehensive review of the methods that form the core of urban informatics from various kinds of urban remote sensing to new approaches to machine learning and statistical modelling. It provides a detailed technical introduction to the wide array of tools information scientists need to develop the key urban analytics that are fundamental to learning about the smart city, and it outlines ways in which these tools can be used to inform design and policy so that cities can become more efficient with a greater concern for environment and equity