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SUMMARY:Probabilistic and Statistical Tools 2 - Christian Soize (Universit
 é Gustave Eiffel)
DTSTART:20230711T090000Z
DTEND:20230711T100000Z
UID:TALK193894@talks.cam.ac.uk
DESCRIPTION:Lecture: Tuesday 11 July 2023\, 10:00 - 11:00Title: Probabilis
 tic and statistical tools 2Presenter: Christian SOIZE\n1. Statistical redu
 ction (PCA and KL expansion).- Principal component analysis (PCA) of a ran
 dom vector.- Numerical construction from a training dataset using a SVD.- 
 Spectral representation (Karhunen-Loeve expansion) of the random field.\n2
 . Brief overview of stochastic solvers for the propagation of uncertaintie
 s.- Why a stochastic solver is not a stochastic modeling process.- First c
 lass of techniques related to Galerkin-type projections.- Second class of 
 techniques related to the direct simulation methods.\n3. Brief overview on
  the fundamental tools for statistical inverse problems.- Description of t
 he problem.- First method: a least square method or the maximum likelihood
  method.- Second method: the Bayesian inference in the nonparametric frame
 work.- Identification scheme with available data coming from experiments.-
  Scheme to identify model-parameter uncertainties from experiments.- Least
 -square method.- Maximum likelihood method for estimating the hyperparamet
 ers.- Asymptotic probability measure of the maximum likelihood estimator.-
  Bayesian inference in a nonparametric framework.- The output-prediction-e
 rror method with an additive Gaussian noise.
LOCATION:Seminar Room 1\, Newton Institute
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