Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763144
Title: Computationally efficient statistical approaches for spatial modelling and high-dimensional emulation of tsunami models
Author: Liu, X.
Awarding Body: UCL (University College London)
Current Institution: University College London (University of London)
Date of Award: 2016
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Abstract:
This thesis addresses some issues in quantifying spatial uncertainties and their propagation through computer models using statistical emulation, motivated by the uncertainty quantification of bathymetry for tsunami modelling. Firstly, we develop a computationally efficient model for spatial data. Gaussian fields (GFs) are frequently used but the associated computational cost can be a bottleneck. The efficient SPDE approach has been proposed by doing the computations using Gaussian Markov random fields (GMRFs) as GFs can be seen as weak solutions to the corresponding stochastic partial differential equations (SPDEs) using piecewise linear finite elements. We introduce a new class of representations of GFs with bivariate splines instead of finite elements. This allows an easier implementation of piecewise polynomial representations of various degrees. It leads to GMRFs that can be inferred efficiently and can be easily extended to non-stationary fields. Secondly, we build statistical emulation for computer models with high-dimensional inputs. In this case, the construction of an emulator can become prohibitively expensive. We propose a joint framework merging emulation with dimension reduction in order to overcome this hurdle. The gradient-based kernel dimension reduction method is chosen for its ability to extract drastically lower dimensions with little loss in information. This generates a low-dimensional process which is emulated with a Gaussian process. The proposed framework is demonstrated to be effective and efficient both theoretically and numerically. Finally, we consider the geostatistical inference of multiple spatial surveys that usually differ in aspects like resolution, accuracy and location. Geoscientific surveys sometimes also present preferential sampling features, which suggest that data locations depend on the values of the spatial field. We propose a joint hierarchical model based on the SPDE approach. This joint model allows us to account for the respective characteristics in each of the surveys separately and thus makes the inference for the underlying spatial process more accurate.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.763144  DOI: Not available
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