Open AccessUse of Wishart Prior and Simple Extensions for Sparse Precision Matrix Estimation
Author(s) -
Markku Kuismin,
Mikko J. Sillanpää
Publication year - 2016
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0148171
Subject(s) - wishart distribution , bayes' theorem , hyperparameter , estimation of covariance matrices , simple (philosophy) , matrix (chemical analysis) , covariance matrix , algorithm , gaussian , computer science , covariance , mathematics , bayesian probability , artificial intelligence , statistics , multivariate statistics , physics , composite material , philosophy , materials science , epistemology , quantum mechanics
A conjugate Wishart prior is used to present a simple and rapid procedure for computing the analytic posterior (mode and uncertainty) of the precision matrix elements of a Gaussian distribution. An interpretation of covariance estimates in terms of eigenvalues is presented, along with a simple decision-rule step to improve the performance of the estimation of sparse precision matrices and associated graphs. In this, elements of the estimated precision matrix that are zero or near zero can be detected and shrunk to zero. Simulated data sets are used to compare posterior estimation with decision-rule with two other Wishart-based approaches and with graphical lasso. Furthermore, an empirical Bayes procedure is used to select prior hyperparameters in high dimensional cases with extension to sparsity.