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math.ST2025
Upper and lower bounds for local Lipschitz stability of Bayesian posteriors
Nada Cvetković, Han Cheng Lie
The work of Sprungk (Inverse Problems, 2020) established the local Lipschitz continuity of the misfit-to-posterior and prior-to-posterior maps with respect to the Kullback--Leibler…
math.ST2025
Optimal low-rank approximations for linear Gaussian inverse problems on Hilbert spaces, Part I: posterior covariance approximation
Giuseppe Carere, Han Cheng Lie
For linear inverse problems with Gaussian priors and Gaussian observation noise, the posterior is Gaussian, with mean and covariance determined by the conditioning formula. Using t…