Parameter estimation in high dimensional Gaussian distributions
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- Aune, E., Simpson, D.P. & Eidsvik, J. Stat Comput (2014) 24: 247. doi:10.1007/s11222-012-9368-y
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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.