- Abstract:
-
This thesis consists of two parts. In the first, we develop two new strategies for spatial white noise and Gaussian-Mat\'ern field sampling that work within a non-nested multilevel (quasi) Monte Carlo (ML(Q)MC) hierarchy. In the second, we apply the techniques developed to quantify the level of uncertainty in a new stochastic model for tracer transport in the brain.
The new sampling techniques are based on the stochastic partial differential equation (SPDE) approach, which recast...
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- Institution:
- University of Oxford
- Division:
- MPLS
- Department:
- Mathematical Institute
- Subgroup:
- Mathematical Institute
- Research group:
- Mathematical and Computational Finance & Numerical Analysis
- Oxford college:
- St Hugh's College
- Role:
- Supervisor
- ORCID:
- 0000-0002-5445-3721
- Institution:
- Simula Research Laboratory
- Subgroup:
- Mathematical Institute
- Research group:
- Department of Numerical Analysis and Scientific Computing
- Role:
- Supervisor
- ORCID:
- 0000-0002-6872-3710
- Institution:
- University of Oxford
- Division:
- MPLS
- Department:
- Mathematical Institute
- Subgroup:
- Mathematical Institute
- Research group:
- Numerical Analysis
- Oxford college:
- Oriel College
- Role:
- Supervisor
- ORCID:
- 0000-0002-1241-7060
- Institution:
- University of Heidelberg
- Research group:
- Numerical Analysis and Uncertainty Quantification
- Role:
- Examiner
- ORCID:
- 0000-0001-8493-4393
- Institution:
- University of Oxford
- Division:
- MPLS
- Department:
- Mathematical Institute
- Subgroup:
- Mathematical Institute
- Research group:
- Numerical Analysis & Oxford Centre for Nonlinear PDE
- Oxford college:
- Worcester College
- Role:
- Examiner
- ORCID:
- 0000-0002-0812-6105
- Grant:
- Programme:
- Oxford-Radcliffe Graduate Scholarships
- Funding agency for:
- Croci, M
- Grant:
- EP/L015803/1
- Programme:
- EPSRC Centre For Doctoral Training in Industrially Focused Mathematical Modelling
- Funding agency for:
- Croci, M
- Type of award:
- DPhil
- Level of award:
- Doctoral
- Awarding institution:
- University of Oxford
- Language:
- English
- Keywords:
- Subjects:
- Copyright holder:
- Croci, M
- Copyright date:
- 2020
Thesis
Multilevel Monte Carlo methods for uncertainty quantification in brain simulations
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Authors
Contributors
+ Giles, MB
+ Rognes, ME
+ Farrell, PE
+ Scheichl, R
+ Suli, E
Funding
+ University College
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+ Engineering and Physical Sciences Research Council
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