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Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix
Turčičová, Marie ; Mandel, J. ; Eben, Kryštof
We present an ensemble filter that provides a rigorous covariance regularization when the underlying random field is Gaussian Markov. We use a linear model for the precision matrix (inverse of covariance) and estimate its parameters together with the analysis mean by the Score Matching method. This procedure provides an explicit expression for parameter estimators. The resulting analysis step formula is the same as in the traditional ensemble Kalman filter.

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