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dc.contributor.authorRuggeri, Fabrizio
dc.contributor.authorSawlan, Zaid A
dc.contributor.authorScavino, Marco
dc.contributor.authorTempone, Raul
dc.date.accessioned2017-06-05T06:02:23Z
dc.date.available2017-06-05T06:02:23Z
dc.date.issued2016-05-12
dc.identifier.citationRuggeri F, Sawlan Z, Scavino M, Tempone R (2017) A Hierarchical Bayesian Setting for an Inverse Problem in Linear Parabolic PDEs with Noisy Boundary Conditions. Bayesian Analysis 12: 407–433. Available: http://dx.doi.org/10.1214/16-BA1007.
dc.identifier.issn1936-0975
dc.identifier.doi10.1214/16-BA1007
dc.identifier.urihttp://hdl.handle.net/10754/624030
dc.description.abstractIn this work we develop a Bayesian setting to infer unknown parameters in initial-boundary 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 time-dependent 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 space-dependent stationary lognormal random field. Synthetic data are used to test the inference. We exploit the behavior of the non-normalized 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.
dc.description.sponsorshipPart of this work was carried out while F. Ruggeri and M. Scavino were Visiting Professors at KAUST. Z. Sawlan, M. Scavino and R. Tempone are members of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.
dc.publisherInstitute of Mathematical Statistics
dc.relation.urlhttp://projecteuclid.org/euclid.ba/1463078272
dc.rightsArchived with thanks to Bayesian Analysis.Creative Commons Attribution 4.0 International License.
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectBayesian inference
dc.subjectHeat equation
dc.subjectLinear parabolic PDEs
dc.subjectNoisy boundary parameters
dc.subjectThermal diffusivity
dc.titleA Hierarchical Bayesian Setting for an Inverse Problem in Linear Parabolic PDEs with Noisy Boundary Conditions
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalBayesian Analysis
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionCNR - IMATI, Consiglio Nazionale delle Ricerche, Milano, , Italy
dc.contributor.institutionInstituto de Estadística (IESTA), Universidad de la República, Montevideo, , Uruguay
dc.identifier.arxivid1501.04739
kaust.personSawlan, Zaid A
kaust.personScavino, Marco
kaust.personTempone, Raul
refterms.dateFOA2018-06-13T18:15:00Z
dc.date.published-online2016-05-12
dc.date.published-print2017-06


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Archived with thanks to Bayesian Analysis.Creative Commons Attribution 4.0 International License.
Except where otherwise noted, this item's license is described as Archived with thanks to Bayesian Analysis.Creative Commons Attribution 4.0 International License.