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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/1078| Stochastic simulation in multimodal posteriors : UQ in ODEs | |
| Javier Enrique Aguilar Romero | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| PROBABILIDAD Y ESTADÍSTICA | |
| Bayesian inference provides a natural and coherent way to quantify uncertainty and knowledge about a phenomenon. It is no surprise the immersion Bayesian statis- tics and Uncertainty Quantification have had in the last years. Metropolis-Hastings provided Bayesian statistics with a powerful tool to calculate intractable integrals and to simulate stochastically from the posterior distribution. However, the inverse problem in Bayesian Uncertainty Quantification deals with the task of numerical in- tegration at each proposed parameter value, which makes exploration of the posterior surface challenging. Moreover the complexity, non linearity and high dimensionality of the forward map induces multimodal posteriors, a typical scene where Metropolis- Hastings fails. Our work addresses and compares different Metropolis-Hastings methods than can be used to approach the multimodality problem. We classify Metropolis-Hastings chains into two big families: Population based and gradient based methods. We present a variety of real life examples of ODEs that present multimodality when solving the inverse problem and the consequences this has when modeling | |
| 01-06-2020 | |
| Trabajo de grado, maestría | |
| OTRAS | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Tesis del CIMAT |
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| Fichero | Descripción | Tamaño | Formato | |
|---|---|---|---|---|
| TE 781.pdf | 34.48 MB | Adobe PDF | Visualizar/Abrir |