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