Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants

By Reinhard Furrer, Thomas Bengtsson. 2007

423 citations recorded by the source corpus.

Subfields: Atmospheric Science, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/fa9d19f0b60ed8f4ec6fb62c7ffdc1389699aef2

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Citations in the corpus

Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems (2008, background): “Moreover, in the Gaussian case, for systems with a ﬁnite number of dominant modes, moderate sample sizes are suﬃcient to accurately estimate posterior means and covariances [12].”
History matching time-lapse seismic data using the ensemble Kalman filter with multiple data assimilations (2012, neutral): “, [2, 17, 44].”
Ensemble Kalman filtering without the intrinsic need for inflation (2011, methodology): “Mallat et al.(1998); Furrer and Bengtsson(2007); Raynaud et al. (2009) put forward a quantitative argument that shows the hortcomings of sampling.”
Improving the Ensemble Estimate of the Kalman Gain by Bootstrap Sampling (2010, background): “Recently, more general methods that do not assume distance dependence of the covariance have been proposed for solving the problem of spurious correlations existing in the ensemble data assimilation method (Anderson 2007; Hacker et al. 2007; Furrer and Bengtsson 2007 ).”
HIGH-DIMENSIONAL COVARIANCE ESTIMATION BY MINIMIZING l1-PENALIZED LOG-DETERMINANT DIVERGENCE BY PRADEEP RAVIKUMAR (2009, neutral): “Submitted to the Annals of Statistics”
Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, methodology): “Furrer et al. (2006) and Furrer and Bengtsson (2007) previously also considered tapering estimators for estimating covariance matrices but in different settings.”
Tapered Covariance: Bayesian Estimation and Asymptotics (2012, background): “Tapering has been studied as a way to speed up computations required for optimal spatial prediction (Furrer, Genton, and Nychka 2006; Furrer and Sain 2009) and for Kalman filter updates (Furrer and Bengtsson 2007).”
An adaptive covariance inflation error correction algorithm for ensemble filters (2007, background): “Most error sources in ensemble filters are expected to lead to underestimates of the ensemble variance (Furrer and Bengtsson, 2006).”
Operator norm consistent estimation of large-dimensional sparse covariance matrices (2008, background): “Various strategies have been proposed (see [ 4 , 17]) that try to take advantage of the assumed structure.”
Positive Definite $\ell_1$ Penalized Estimation of Large Covariance Matrices (2012, methodology): “…have been used to improve the sample covariance matrix estimator, including banding (Wu and Pourahmadi, 2003; Bickel and Levina, 2008a), tapering (Furrer and Bengtsson, 2007; Cai, Zhang, and Zhou, 2010) and thresholding (Bickel and Levina, 2008b; El Karoui, 2008; Rothman, Levina, and Zhu, 2009).”
Localization and regularization for iterative ensemble smoothers (2017, methodology): “2 a GC taper function [15], b and c taper function in Furrer and Bengtsson [14] with Spherical and Gaussian covariance function with ensemble size of 20 (black dashed), 100 (blue solid), and 1000 (red dash-dotted)”
Global Testing and Large-Scale Multiple Testing for High-Dimensional Covariance Structures (2017, methodology): “These include the banding methods in Wu and Pourahmadi (2009) and Bickel and Levina (2008a), tapering in Furrer and Bengtsson (2007) and Cai et al. (2010), thresholding rules in Bickel and Levina (2008b), El Karoui (2008), Rothman et al. (2009), Cai and Liu (2011), and Fan et al. (2011), penalized…”