HLIBCov: Parallel Hierarchical Matrix Approximation of Large Covariance Matrices and Likelihoods with Applications in Parameter Identification
For practitioners in geostatistics and spatial statistics, this enables scalable parameter estimation for massive datasets.
The paper presents HLIBCov, a package that uses parallel hierarchical matrices to estimate covariance parameters (variance, smoothness, covariance length) by maximizing Gaussian log-likelihood, achieving log-linear cost for large matrices. It demonstrates parameter identification for 2,000,000 locations on a PC-desktop.
We provide more technical details about the HLIBCov package, which is using parallel hierarchical ($\H$-) matrices to identify unknown parameters of the covariance function (variance, smoothness, and covariance length). These parameters are estimated by maximizing the joint Gaussian log-likelihood function. The HLIBCov package approximates large dense inhomogeneous covariance matrices with a log-linear computational cost and storage requirement. We explain how to compute the Cholesky factorization, determinant, inverse and quadratic form in the H-matrix format. To demonstrate the numerical performance, we identify three unknown parameters in an example with 2,000,000 locations on a PC-desktop.