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dc.contributor.authorNickl, Richarden
dc.date.accessioned2018-09-08T06:30:52Z
dc.date.available2018-09-08T06:30:52Z
dc.identifier.issn1435-9855
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/279802
dc.description.abstract© European Mathematical Society 2020 We consider the inverse problem of determining the potential f > 0 in the partial differential equation 1 2 u − fu = 0 on O, u = g on ∂O, where O is a bounded C∞-domain in Rd and g > 0 is a given function prescribing boundary values. The data consist of the solution u corrupted by additive Gaussian noise. A nonparametric Bayesian prior for the function f is devised and a Bernstein-von Mises theorem is proved which entails that the posterior distribution given the observations is approximated in a suitable function space by an infinite-dimensional Gaussian measure that has a 'minimal' covariance structure in an information-theoretic sense. As a consequence the posterior distribution performs valid and optimal frequentist statistical inference on various aspects of f in the small noise limit.
dc.publisherEuropean Mathematical Society
dc.titleBernstein-von Mises theorems for statistical inverse problems I: Schrödinger equationen
dc.typeArticle
prism.endingPage2750
prism.issueIdentifier8en
prism.publicationNameJournal of the European Mathematical Societyen
prism.startingPage2697
prism.volume22en
dc.identifier.doi10.17863/CAM.27172
rioxxterms.versionofrecord10.4171/JEMS/975en
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEuropean Commission (647812)
cam.issuedOnline2020-05-28en
rioxxterms.freetoread.startdate2019-09-07


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