A homogenization-surrogate ensemble Kalman filter converges to the exact multiscale ensemble Kalman filter at rate O(ε + h^(s+1)), with the empirical posteriors converging in Wasserstein distance.
Abdulle, A priori and a posteriori error analysis for numerical homogenization: a unified framework, Ser
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Ensemble Kalman filter for multiscale inverse problems
A homogenization-surrogate ensemble Kalman filter converges to the exact multiscale ensemble Kalman filter at rate O(ε + h^(s+1)), with the empirical posteriors converging in Wasserstein distance.