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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/1127| On Uncertainty Quantification of Models Defined by Initial and Boundary Value Problems for Differential Equations | |
| HUGO ALBERTO FLORES ARGUEDAS | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| MATEMÁTICAS APLICADAS Uncertainty Quantification Bayesian Inverse Problems | |
| Inverse problems arise in an enormous variety of science and engineering applications where model parameters must be estimated from noisy and indirect observational data. These problems are characterized by observational errors, model errors, and issues of ill-posedness which yield uncertainties in model parameters. Bayesian statistical approaches to inverse problems allow us to make simulations and predictions with quantified uncertainties. These tasks become essential in model-based decision-making. Using a dynamical system based on physical principles to predict the observations is known as the forward problem. Traditional Bayesian methods as inference of the parameters, sampling from a distribution, quadrature approximations, experimental design, and model selection are affected by the introduction of a numerical solution of an ODE/PDE system. Therefore, ensuring the regularity of the direct problem, the consistency in the discretization, and the consequent stability of the posterior is of great importance to building reliable predictions. In this work, our specific interest relies on the challenges for the statistical approach for inverse problems defined by initial and boundary value problems for differential equations. We present several examples of inverse problems with applications in mesh refinement, elastography, epidemics, and biology. To face these problems, we consider model selection criteria, experimental design strategies, posterior sampling schemes, among others in which we apply dimension reduction, optimization, and numerical analysis tools. The main goal illustrated by these examples is the systematic treatment of model, data, and computational errors to produce predictions with quantified uncertainty. | |
| 19-03-2021 | |
| Trabajo de grado, doctorado | |
| OTRAS | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Tesis del CIMAT |
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