Change-point detection for a transient change and high-dimensional covering

Noonan, Jack 2021. Change-point detection for a transient change and high-dimensional covering. PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

This thesis is divided into two parts. Part one is the major contribution of this thesis and considers the topic of change-point detection. The majority of research in Part one focuses on deriving certain quantities for a particular change-point detection procedure. The derivation of these quantities relies on the ability to evaluate (or approximate) complicated boundary crossing probabilities for a particular Gaussian process. Part two is a topic of extra interest and studies the covering and quantization of high dimensional sets. As the main problem, we consider the covering and quantization of a d-dimensional cube by n balls with reasonably large d (10 or more) and reasonably small n, like n = 100. When considering covering problems, the full coverage is not enforced but instead, only 95% or 99% coverage is desired. The results of Part two establish that efficient covering schemes have several important properties which are not seen in small dimensions and in asymptotical considerations, for very large n. One of these properties can be termed `do not try to cover the vertices' as the vertices of the cube and their close neighbourhoods are very hard to cover and for large d there are too many of them. The structure and content of this thesis is based on the eight published papers of the author; the relevant paper is referenced at the start of each chapter.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Funders:	EPSRC
Date of First Compliant Deposit:	23 September 2021
Last Modified:	23 Sep 2021 12:49
URI:	https://orca.cardiff.ac.uk/id/eprint/144326

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