Bayesian approaches to modelling physical and socio-economic systems

Abstract

Modelling, simulation and experimentation are each important to understand the world that we live in. The world itself is a complex system, although the physical and socio-economic systems within are usually studied separately with a particular objective in mind. Owing to economic, practical and ethical considerations, experimentation and direct measurement are not always possible for these systems. Instead, a mathematical model can be used to retrieve the unknown quantities of interest from indirect measurement data, and to study how the system will behave in a number of different scenarios. Both tasks require solving the so-called parameter estimation problem. There are a number of uncertainties encountered in the modelling process, including those introduced by the mathematical model and its numerical simulation, and those present in the measurement data. A statistical approach to parameter estimation allows these uncertainties to be formally accounted for. There are a number advantages for using the Bayesian framework, although there are usually non-trivial statistical and computational challenges that must first be overcome. In this thesis, some new Bayesian approaches are developed to provide improved modelling capabilities for physical and socio-economic systems. The systems studied in this thesis involve spatially-distributed data, which includes the estimation of a spatially varying parameter via a complex function, parameter estimation for high-dimensional Gaussian models and uncertainty quantification for urban simulations. Monte Carlo methods are used throughout to obtain accurate summaries of the complex probability distributions involved. The new approaches are demonstrated with empirical simulation studies. Whilst the new approaches are shown to provide improvements on the existing ones, Bayesian inference remains a challenging and computationally intensive task. Further work is suggested to accelerate Bayesian inference, so that inferences can be made on more practical time scales.