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时间:2019-07-09
《Generalized priors in Bayesian inversion problems》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、AdvancesinWaterResources36(2012)3–10ContentslistsavailableatScienceDirectAdvancesinWaterResourcesjournalhomepage:www.elsevier.com/locate/advwatresGeneralizedpriorsinBayesianinversionproblemsPeterK.KitanidisStanfordUniversity,CivilandEnvironmentalEngineering,473ViaOrtega,Stanford,
2、CA94305,UnitedStatesarticleinfoabstractArticlehistory:Inverseproblems,whenonlyharddataareconsidered,aremathematicallyill-posedbecausetheyhaveAvailableonline14June2011multiplesolutionsandaresensitivetosmallchangesinthedata.Anexampleisthedeterminationofhydraulicconductivityfromhead
3、data.BayesianmethodsprovideageneralstochasticframeworkwithinKeywords:whichonecansolvesuchproblems.Theapproachallowsonetocombineharddatawithotherinforma-Inversemodelingtioninordertoexploretherangeofpossiblesolutions.Weconsidertheroleofgeneralized(alsoknownInterpolationasimproper)p
4、robabilitydistributionswithinthisframework.ThesedistributionsareveryusefulbecauseProbabilisticanalysistheyrepresentinformationparsimoniously(withsimpleequationsandfewparameters)andareidealinUncertaintyquantificationtermsofrepresentingsituationswithlimitedinformation.Theyareparticu
5、larlyusefulinintroducingpriorinformationaboutthedependentvariablesoftheinverseproblemandstructuralparametersthatdescribethedegreeofcontinuityorsmoothnessofdependentvariables.Additionally,theyareveryusefulfromacomputationalperspectivebecausetheycanleadtoformulationswithspecialstru
6、cture,suchaswithhighdegreeofsparsityorstructurethatcanbeexploitedthroughhighperformancecomputingalgorithms.Weexamineinthecontextofasimpleexamplesomeoftheconsequencesofusingdifferentgeneralizedpriors.Ó2011ElsevierLtd.Allrightsreserved.1.Inverseproblems2pty1¼ecosð3ÞTTheterminvers
7、eproblemissometimesusedassynonymforparameterestimation.AlthoughthismaybeavaliddescriptionThen,thesolutionisinsomecases,adistinguishingfeatureofaninverseproblemisdy02pe2ptthatitismathematicallyill-posedinthesenseofHadamard.SuchsðtÞ¼sinð4ÞdtTTproblemsarestudiedin,forexample,Laur
8、ientiev[17].Aproblemissaidtobewellposedi
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