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Bayesian Parameter Estimation via Filtering and Functional Approximations
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The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a filter acting on random variables, and while its Monte Carlo variant --- the Ensemble Kalman Filter (EnKF) --- is fairly straightforward, we subsequently only sketch its implementation with the help of functional representations.
Forward citations
Cited by 2 Pith papers
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Mechanical State Estimation with a Polynomial-Chaos-Based Statistical Finite Element Method
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Reduced Order Models and Conditional Expectation -- Analysing Parametric Low-Order Approximations
Parametric reduced-order models built by least-squares projection, including POD, reduced basis methods, and Gaussian process emulation, can be viewed as conditional expectations in a Bayesian updating framework.
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