What is it about?
We describe the method and provide implementation details. 1. We use parallel hierarchical (H-) matrices to approximate large covariance matrices of the Matern type. 2. Then we compute the Cholesky factorisation, matrix-determinant, MV product, quadratic form, the inverse, the joint Gaussian likelihood. Everything in the H-matrix format. 3. We search the maximum of the joint Gaussian log-likelihood. This is a non-linear function, depending in a non-linear way on 3 parameters of the Matern covariance. 4. We research how the H-matrix approximation accuracy influences the confidence intervals for parameter estimates. See also https://www.hlibpro.com/doc/2.7/TUTORLoglikelyhood.html Reproducible updated code https://github.com/litvinen/large_random_fields
Photo by Markus Spiske on Unsplash
Why is it important?
Estimation of unknown parameters is fundamental engineering, medical, chemical, geological, weather prediction problem. The maximum likelihood estimation (MLE) method is a well known and very often used method. The drawback is that it requires very expensive matrix arithmetic, with O(n^3) computing cost and storage. The usage of the H-matrix technique allows us to avoid this drawback. The new storage and complexity are O(n log n).
Read the Original
This page is a summary of: HLIBCov: Parallel hierarchical matrix approximation of large covariance matrices and likelihoods with applications in parameter identification, MethodsX, July 2019, Elsevier, DOI: 10.1016/j.mex.2019.07.001.
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HLIBCov: Parallel hierarchical matrix approximation of large covariance matrices and likelihoods with applications in parameter identification
Elsevier MethodsX journal
To download software with examples
It is implemented as a standard example in the HLIBPro library, well-documented, well-tuned code!
Github repository with the updated source code (2021)
In this repository you can find th source code for this competition "KAUST Competition on Spatial Statistics for Large Datasets" https://cemse.kaust.edu.sa/stsds/kaust-competition-spatial-statistics-large-datasets
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