The Bayesian Approach to Inverse Problem

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1、TheBayesianApproachtoInverseProblemsAndrewM.StuartMathematicsInstituteWarwickUniversityCV47AL,UKa.m.stuart@warwick.ac.ukAbstract:Theselecturenotesprovideanintroductiontotheforthcomingbook[DHS13].Contents1Introduction............................................

2、.....21.1BayesianInversionRn........................................21.2InverseHeatEquation........................................31.3EllipticInverseProblem.......................................42PriorModeling...............................................52

3、.1GeneralSetting............................................52.2UniformPriors............................................52.3BesovPriors..............................................62.4GaussianPriors............................................82.5Summary.....

4、..........................................103PosteriorDistribution...........................................113.1ConditionedRandomVariables...................................113.2BayesTheoremforInverseProblems................................123.3HeatEquation.

5、...........................................123.4EllipticInverseProblem.......................................134CommonStructure.............................................154.1Well-Posedness............................................154.2Approximation.......

6、.....................................184.3MeasurePreservingDynamics....................................194.3.1FiniteDimensionalCase...................................204.3.2InniteDimensionalCase..................................214.3.3ChangeofMeasure.........

7、.............................224.3.4UsefulProperties.......................................234.3.5TheInvarianceResult....................................244.4MCMCMethods...........................................275BibliographicalNotes.........................

8、..................28References....................................................301imsart-genericver.2007/12/10file:lecturenotes.texdate:August2,20121.Introduction1.1.BayesianInv