eprintid: 10192808
rev_number: 13
eprint_status: archive
userid: 699
dir: disk0/10/19/28/08
datestamp: 2024-10-04 06:24:08
lastmod: 2024-10-04 06:24:08
status_changed: 2024-10-04 06:24:08
type: thesis
metadata_visibility: show
sword_depositor: 699
creators_name: Li, Kaiyu
title: Multilevel Methods for Monte Carlo Integration, with Applications to Tsunami Modelling
ispublished: unpub
divisions: UCL
divisions: B04
divisions: C06
divisions: F61
note: Copyright © The Author 2024.  Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/).  Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms.  Access may initially be restricted at the author’s request.
abstract: In this thesis, we first propose a new method called multilevel Bayesian quadrature (MLBQ). MLBQ enhances multilevel Monte Carlo (MLMC) through Gaussian process models and the associated Bayesian quadrature estimators. Using both theory and numerical experiments, including a landslide-generated tsunami modelling example, we show that MLBQ leads to significant improvements in accuracy over MLMC when the integrand is expensive and smooth and when the dimension is small or moderate. Then, a high-resolution numerical model is employed to simulate future tsunamis in Sumatra, Indonesia. We output momentum flux (a combination of velocity and height of the tsunami) as a better intensity measure of tsunami impacts. Using MLBQ, we account for the influence of uncertain land cover roughness, which is considered fixed in the tsunami simulator. We also construct Gaussian process emulators to predict future inundation in Sumatra, Indonesia. Using a catastrophe modelling framework, the results are used to provide health and financial impact prediction in Sumatra, Indonesia. Considering the limitations of MLBQ, such as requiring closed-form kernel means, we propose an alternative method that uses kernel-based control variates to reduce the variance of MLMC. We call this method multilevel control functional (MLCF). MLCF is more widely applicable. We demonstrate that MLCF surpasses MLMC in terms of accuracy through theory and empirical assessments, including a Bayesian inference example.
date: 2024-05-28
date_type: published
full_text_type: other
thesis_class: doctoral_embargoed
thesis_award: Ph.D
language: eng
verified: verified_manual
elements_id: 2278765
lyricists_name: Li, Kaiyu
lyricists_id: KLIAX45
actors_name: Li, Kaiyu
actors_id: KLIAX45
actors_role: owner
full_text_status: restricted
pages: 159
institution: UCL (University College London)
department: Statistical Science
thesis_type: Doctoral
citation:        Li, Kaiyu;      (2024)    Multilevel Methods for Monte Carlo Integration, with Applications to Tsunami Modelling.                   Doctoral thesis  (Ph.D), UCL (University College London).    
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10192808/7/PhD_Thesis.pdf