%0 Journal Article %1 aune2014parameter %A Aune, Erlend %A Simpson, Daniel P. %A Eidsvik, Jo %D 2014 %J Statistics and Computing %K Gaussian_processes linear_algebra methods statistics %N 2 %P 247--263 %R 10.1007/s11222-012-9368-y %T Parameter estimation in high dimensional Gaussian distributions %U https://doi.org/10.1007/s11222-012-9368-y %V 24 %X In order to compute the log-likelihood for high dimensional Gaussian models, it is necessary to compute the determinant of the large, sparse, symmetric positive definite precision matrix. Traditional methods for evaluating the log-likelihood, which are typically based on Cholesky factorisations, are not feasible for very large models due to the massive memory requirements. We present a novel approach for evaluating such likelihoods that only requires the computation of matrix-vector products. In this approach we utilise matrix functions, Krylov subspaces, and probing vectors to construct an iterative numerical method for computing the log-likelihood.

@article{aune2014parameter, abstract = {In order to compute the log-likelihood for high dimensional Gaussian models, it is necessary to compute the determinant of the large, sparse, symmetric positive definite precision matrix. Traditional methods for evaluating the log-likelihood, which are typically based on Cholesky factorisations, are not feasible for very large models due to the massive memory requirements. We present a novel approach for evaluating such likelihoods that only requires the computation of matrix-vector products. In this approach we utilise matrix functions, Krylov subspaces, and probing vectors to construct an iterative numerical method for computing the log-likelihood.}, added-at = {2021-01-20T22:17:19.000+0100}, author = {Aune, Erlend and Simpson, Daniel P. and Eidsvik, Jo}, biburl = {https://www.bibsonomy.org/bibtex/2e41fee053c0b05368b4aa0f2531b5e46/peter.ralph}, day = 01, doi = {10.1007/s11222-012-9368-y}, interhash = {766a33cc47165f0a8f047a1e90d0055b}, intrahash = {e41fee053c0b05368b4aa0f2531b5e46}, issn = {1573-1375}, journal = {Statistics and Computing}, keywords = {Gaussian_processes linear_algebra methods statistics}, month = mar, number = 2, pages = {247--263}, timestamp = {2021-01-20T22:17:19.000+0100}, title = {Parameter estimation in high dimensional {Gaussian} distributions}, url = {https://doi.org/10.1007/s11222-012-9368-y}, volume = 24, year = 2014 }