TY - JOUR
T1 - Parameter estimation in high dimensional Gaussian distributions
AU - Aune, Erlend
AU - Simpson, Daniel P.
AU - Eidsvik, Jo
PY - 2014/3
Y1 - 2014/3
N2 - 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.
AB - 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.
UR - http://dx.doi.org/ 10.1007/s11222-012-9368-y
U2 - 10.1007/s11222-012-9368-y
DO - 10.1007/s11222-012-9368-y
M3 - Article
SN - 0960-3174
VL - 24
SP - 247
EP - 263
JO - Statistics and Computing
JF - Statistics and Computing
IS - 2
ER -