Stochastic ordering and sparse approximation of multivariate extremal dependence
Lead Research Organisation:
CARDIFF UNIVERSITY
Department Name: Sch of Mathematics
Abstract
This studentship will develop a paradigm-changing theoretical underpinning of novel tools for assessing extremal dependence in high dimensions. It is based on extending a recently discovered link between classical principal component analysis and multivariate extreme value theory.
While most statistical tools that have a strong theoretical underpinning characterise the typical behaviour of a system, in many practical or safety-critical situations it is instead the extreme behaviours and their dependence, which require particular attention. Contrary to public perception, examples of such settings are ubiquitous and an improved understanding aided by sound statistical procedures is of utmost importance, for instance to assess risk related to environmental hazards, network failure or financial portfolio losses. What complicates such tasks is the lack of generic and interpretable, theoretically well-studied and computationally feasible statistical tools to explore the extremal dependence structure of high-dimensional data.
While most statistical tools that have a strong theoretical underpinning characterise the typical behaviour of a system, in many practical or safety-critical situations it is instead the extreme behaviours and their dependence, which require particular attention. Contrary to public perception, examples of such settings are ubiquitous and an improved understanding aided by sound statistical procedures is of utmost importance, for instance to assess risk related to environmental hazards, network failure or financial portfolio losses. What complicates such tasks is the lack of generic and interpretable, theoretically well-studied and computationally feasible statistical tools to explore the extremal dependence structure of high-dimensional data.
Organisations
People |
ORCID iD |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/V520159/1 | 30/09/2020 | 31/10/2025 | |||
| 2435137 | Studentship | EP/V520159/1 | 30/09/2020 | 29/09/2024 |
| Description | While traditional statistical methodologies focus on the average behaviour of a system and quantifying deviations from it, practical concern often lies on the extremal behaviour of a system (e.g. when quantifying flood risks or the riskiness of a financial position). This thesis is concerned with methods to study the likely behaviour of a system when several components can be extreme together. There are two main outcomes. Both are on a very fundamental level and help dealing with situations when the number of variables are very large. One is a better understanding of how a range of relevant models for extreme behaviour are ordered. Such findings are important when one wants to draw robust conclusions about the stochastic behaviour of a system when only partial knowledge is available. They have been presented recently at the Mathematical research center at Oberwolfach and entered the corresponding Oberwolfach report: https://publications.mfo.de/handle/mfo/4173. The second outcome are about new methodology how to compress data about dependencies between the variables quickly and with least possible loss of information. In order to achieve this ideas from machine learning have been successfully transferred to this context. |
| Exploitation Route | The outcomes can help on the one hand in exploratory data analysis for extreme values and facilitate detection of directions in which variables may be large simultaneously. On the other hand, they can help to draw more robust conclusions about probabilities of rare events that have a compound nature. So far, numerical experiments evidence the good performance. The next step will be to run further case studies and test cases. |
| Sectors | Construction Digital/Communication/Information Technologies (including Software) Energy Environment Financial Services and Management Consultancy Transport |