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| Partial differential equations with random parameters play a great role in uncertainty quantification. As the random parameters are often not known exactly and not directly
observable, one has to solve a stochastic inverse problem in an infinite dimensional
space. One recent approach to tackle this problem uses Bayesian techniques, which
result in complicated and expensive calculations. Therefore in the literature some approximate
methods for the Bayesian inversion problem, like Ensemble Kalman Filter (EnKF) or
Polynomial Chaos Expansion Kalman Filter (PCE-KF) were proposed, but without sound mathematical foundation. In the talk the stochastic model underlying these methods is given and it is shown, that they usually cannot solve the problem of full Bayesian inversion. |
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