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Activity Number:
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359
- Advances in Spatial and Spatio-Temporal Statistics
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Type:
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Contributed
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Date/Time:
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Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
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Sponsor:
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Section on Statistics and the Environment
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Abstract #312863
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Title:
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Hierarchical Sparse Cholesky Decomposition with Applications to High-Dimensional Spatio-Temporal Filtering
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Author(s):
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Marcin Jurek* and Matthias Katzfuss
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Companies:
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Texas A & M University and Texas A&M University
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Keywords:
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state-space model;
spatio-temporal statistics;
hierarchical matrices;
Vecchia approximation;
data assimilation;
sparse Cholesky decomposition
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Abstract:
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Cholesky decomposition is a common matrix operation in the analysis of spatial data. 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 equivalent sparsity in the Cholesky factor of 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.
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Authors who are presenting talks have a * after their name.
