Complete Deterministic Dynamics and Spectral Decomposition of the Linear Ensemble Kalman Inversion

نویسندگان

چکیده

The ensemble Kalman inversion (EKI) for the solution of Bayesian inverse problems type , with being an unknown parameter, a given datum, and measurement noise, is powerful tool usually derived from sequential Monte Carlo point view. It describes dynamics particles whose initial empirical measure sampled prior, evolving over artificial time toward approximate problem, emulating posterior, corresponding to underregularized minimum-norm problem. Using spectral techniques, we provide complete description deterministic EKI its asymptotic behavior in parameter space. In particular, analyze naive mean-field special focus on their behavior. Furthermore, show that—even case—residuals space do not decrease monotonously Euclidean norm suggest problem-adapted norm, where monotonicity can be proved. Finally, derive system ordinary differential equations governing spectrum eigenvectors covariance matrix. While analysis aimed at EKI, believe that it applied understand more general particle-based dynamical systems.

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ژورنال

عنوان ژورنال: SIAM/ASA Journal on Uncertainty Quantification

سال: 2023

ISSN: ['2166-2525']

DOI: https://doi.org/10.1137/21m1429461