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.
- NSF-PAR ID:
- 10425744
- Date Published:
- Journal Name:
- Journal of Data Science
- ISSN:
- 1680-743X
- Page Range / eLocation ID:
- 461 to 474
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This article is categorized under:
Algorithms and Computational Methods > Algorithms
Algorithms and Computational Methods > Numerical Methods
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