Li, Kaiyu; (2024) Multilevel Methods for Monte Carlo Integration, with Applications to Tsunami Modelling. Doctoral thesis (Ph.D), UCL (University College London).

Text PhD_Thesis.pdf - Other Access restricted to UCL open access staff until 1 June 2025. Download (18MB)

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.

Download activity - last month

Export as CSVXMLJSON

Download activity - last 12 months

Export as JSONXMLCSV

Downloads by country - last 12 months

Export as CSVXMLJSON

Archive Staff Only

View Item