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SDS Seminar Series: Dr. Marcin Jurek (Friday 4/30/21, 2pm)
Friday, April 30, 2021, 02:00pm - 03:00pm

The Spring 2021 SDS Seminar Series continues on Friday, April 30 from 2:00 p.m. to 3:00 p.m. via Zoom with Dr. Marcin Jurek (Postdoctoral Fellow at the Department of Statistics and Data Sciences in the College of Natural Sciences at The University of Texas at Austin).

Please contact stat.admin@austin.utexas.edu for the Zoom link.

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Title: Hierarchical sparse Cholesky decomposition with applications to high-dimensional spatio-temporal filtering

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 spatio-temporal filtering. We present a fast and simple algorithm to compute our hierarchical Vecchia approximation, and we provide extensions to non-linear data assimilation with non-Gaussian data based on the Laplace approximation. In several numerical comparisons, our methods strongly outperformed alternative approaches.