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Creators/Authors contains: "Katzfuss, Matthias"

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  1. Free, publicly-accessible full text available June 30, 2023
  2. Abstract Spatial statistics often involves Cholesky decomposition of covariance matrices. To ensure scalability to high dimensions, several recent approximations have assumed a sparse Cholesky factor of the precision matrix. We propose a hierarchical Vecchia approximation, whose conditional-independence assumptions imply sparsity in the Cholesky factors of both the precision and the covariance matrix. This remarkable property is crucial for applications to high-dimensional spatiotemporal filtering. We present a fast and simple algorithm to compute our hierarchical Vecchia approximation, and we provide extensions to nonlinear data assimilation with non-Gaussian data based on the Laplace approximation. In several numerical comparisons, including a filtering analysis of satellite data, our methods strongly outperformed alternative approaches.
    Free, publicly-accessible full text available February 15, 2023
  3. Free, publicly-accessible full text available October 2, 2022
  4. Abstract The ensemble Kalman filter (EnKF) is a popular technique for data assimilation in high-dimensional nonlinear state-space models. The EnKF represents distributions of interest by an ensemble, which is a form of dimension reduction that enables straightforward forecasting even for complicated and expensive evolution operators. However, the EnKF update step involves estimation of the forecast covariance matrix based on the (often small) ensemble, which requires regularization. Many existing regularization techniques rely on spatial localization, which may ignore long-range dependence. Instead, our proposed approach assumes a sparse Cholesky factor of the inverse covariance matrix, and the nonzero Cholesky entries are further regularized. The resulting method is highly flexible and computationally scalable. In our numerical experiments, our approach was more accurate and less sensitive to misspecification of tuning parameters than tapering-based localization.