Bayesian approaches to modelling physical and socio-economic systems
File(s)
Author(s)
Ellam, Louis
Type
Thesis
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.
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.
Version
Open Access
Date Issued
2018-11
Date Awarded
2019-05
Copyright Statement
Creative Commons Attribution NonCommercial Licence
Advisor
Girolami, Mark
Pavliotis, Grigorios
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)