SRI  Center for Uncertainty Quantification
in Computational Science & Engineering
Home
About
People
Faculty
Visiting Professors
Consultants
Research Scientists
Postdoctoral Fellows
Students
Visiting Students
Staff
Member of the Board
Previous Members
Research
Research Projects
Posters
Publications
Books
Book Chapters
Conference Proceedings
Manuscripts
Refereed Journals
Technical Reports
Events
Calendar
Gallery
KAUST UQ School 2016
Zavala's Seminar and Short Course
Grossmann’s Seminars and Short Course
UQ Annual Workshop 2016
UQ Annual Workshop 2015
Spatial Statistics Workshop 2014
UQ Annual Workshop 2014
UQ Annual Workshop 2013
News
Courses
Spring 2016
Summer 2015
Fall 2015
Seminars
Join Us
Links
Home
>
Publications
>
Refereed Journals
>
A hierarchical Bayesian setting for an inverse problem in linear parabolic PDEs with noisy boundary conditions
Publications
A hierarchical Bayesian setting for an inverse problem in linear parabolic PDEs with noisy boundary conditions
Bibliography:
Bibliography
F. Ruggeri, Z. Sawlan, M. Scavino, R. Tempone,
A hierarchical Bayesian setting for an inverse problem in linear parabolic PDEs with noisy boundary conditions,
Bayesian Analysis, Advance Publication, 12 May 2016. doi: 10.1214/16BA1007
Authors:
F. Ruggeri, Z. Sawlan, M. Scavino, R. Tempone
Keywords:
A hierarchical Bayesian setting for an inverse problem in linear parabolic PDEs with noisy boundary conditions
Year:
2017
Abstract:
In this work we develop a Bayesian setting to infer unknown parameters in initialboundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given prescribed initial condition. We show how to derive the joint likelihood function for the forward problem, given some measurements of the solution field subject to Gaussian noise. Given Gaussian priors for the timedependent Dirichlet boundary values, we analytically marginalize the joint likelihood using the linearity of the equation. Our hierarchical Bayesian approach is fully implemented in an example that involves the heat equation. In this example, the thermal diffusivity is the unknown parameter. We assume that the thermal diffusivity parameter can be modeled a priori through a lognormal random variable or by means of a spacedependent stationary lognormal random field. Synthetic data are used to test the inference. We exploit the behavior of the nonnormalized log posterior distribution of the thermal diffusivity. Then, we use the Laplace method to obtain an approximated Gaussian posterior and therefore avoid costly Markov Chain Monte Carlo computations. Expected information gains and predictive posterior densities for observable quantities are numerically estimated using Laplace approximation for different experimental setups.
ISSN:
2017
https://projecteuclid.org/euclid.ba/1463078272
https://projecteuclid.org/euclid.ba/1463078272
No
Site Map

Privacy Policy

Terms of Use

Team Site
©
2021
King Abdullah University of Science and Technology,
All rights reserved.
SRI  Center for Uncertainty Quantification
in Computational Science & Engineering
http://
http://