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A multiscale framework for Bayesian inference in elliptic problems

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dc.contributor.advisor Youssef Marzouk. en_US Parno, Matthew David en_US
dc.contributor.other Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US 2011-08-18T19:18:37Z 2011-08-18T19:18:37Z 2011 en_US 2011 en_US
dc.description Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2011. en_US
dc.description Page 118 blank. Cataloged from PDF version of thesis. en_US
dc.description Includes bibliographical references (p. 112-117). en_US
dc.description.abstract The Bayesian approach to inference problems provides a systematic way of updating prior knowledge with data. A likelihood function involving a forward model of the problem is used to incorporate data into a posterior distribution. The standard method of sampling this distribution is Markov chain Monte Carlo which can become inefficient in high dimensions, wasting many evaluations of the likelihood function. In many applications the likelihood function involves the solution of a partial differential equation so the large number of evaluations required by Markov chain Monte Carlo can quickly become computationally intractable. This work aims to reduce the computational cost of sampling the posterior by introducing a multiscale framework for inference problems involving elliptic forward problems. Through the construction of a low dimensional prior on a coarse scale and the use of iterative conditioning technique the scales are decouples and efficient inference can proceed. This work considers nonlinear mappings from a fine scale to a coarse scale based on the Multiscale Finite Element Method. Permeability characterization is the primary focus but a discussion of other applications is also provided. After some theoretical justification, several test problems are shown that demonstrate the efficiency of the multiscale framework. en_US
dc.description.statementofresponsibility by Matthew David Parno. en_US
dc.format.extent 118 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri en_US
dc.subject Computation for Design and Optimization Program. en_US
dc.title A multiscale framework for Bayesian inference in elliptic problems en_US
dc.type Thesis en_US S.M. en_US
dc.contributor.department Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US
dc.identifier.oclc 746081025 en_US

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