Statistics and Computing

, Volume 24, Issue 2, pp 247–263

Parameter estimation in high dimensional Gaussian distributions


DOI: 10.1007/s11222-012-9368-y

Cite this article as:
Aune, E., Simpson, D.P. & Eidsvik, J. Stat Comput (2014) 24: 247. doi:10.1007/s11222-012-9368-y


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.


Gaussian distributionKrylov methodsMatrix functionsNumerical linear algebraEstimation

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Norwegian University of Science and TechnologyTrondheimNorway