Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix

0551812 - ÚI 2022 RIV US eng J - Článek v odborném periodiku
Turčičová, Marie - Mandel, J. - Eben, Kryštof
Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix.
Foundations of Data Science. Roč. 3, č. 4 (2021), s. 793-824. E-ISSN 2639-8001
Grant CEP: GA TA ČR(CZ) TL01000238; GA TA ČR(CZ) TO01000219
Institucionální podpora: RVO:67985807
Klíčová slova: Score matching * ensemble filter * Gaussian Markov random field * covariance modelling
Obor OECD: Statistics and probability
Způsob publikování: Open access
http://dx.doi.org/10.3934/fods.2021030

We present an ensemble filtering method based on a linear model for the precision matrix (the inverse of the covariance) with the parameters determined by Score Matching Estimation. The method provides a rigorous covariance regularization when the underlying random field is Gaussian Markov. The parameters are found by solving a system of linear equations. The analysis step uses the inverse formulation of the Kalman update. Several filter versions, differing in the construction of the analysis ensemble, are proposed, as well as a Score matching version of the Extended Kalman Filter.
Trvalý link: http://hdl.handle.net/11104/0327033