Optimal low-rank approximations to the posterior mean (with fixed covariance) and joint mean-covariance are derived for linear Gaussian inverse problems on separable Hilbert spaces, with equivalence conditions and projector interpretations.
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Derives error bounds on the root prior-preconditioned Hessian, posterior covariance, and mean for a Petrov-Galerkin reduced-order model, with exact posterior recovery at the intrinsic dimension.
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Optimal low-rank posterior mean and distribution approximation in linear Gaussian inverse problems on Hilbert spaces
Optimal low-rank approximations to the posterior mean (with fixed covariance) and joint mean-covariance are derived for linear Gaussian inverse problems on separable Hilbert spaces, with equivalence conditions and projector interpretations.