Use of Wishart Prior and Simple Extensions for Sparse Precision Matrix Estimation

PloS One
Markku Kuismin, Mikko J Sillanpää

Abstract

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.

References

Mar 25, 2000·Journal of the Society for Gynecologic Investigation·D P EdwardsE Gass-Handel
Dec 15, 2007·Biostatistics·Jerome FriedmanRobert Tibshirani
May 25, 2012·TAG. Theoretical and applied genetics. Theoretische und angewandte Genetik·Zitong Li, Mikko J Sillanpää
Oct 11, 2012·Biometrika·Jacob Bien, Robert J Tibshirani
Jun 5, 2013·Journal of the Royal Statistical Society. Series B, Statistical Methodology·Joong-Ho WonBala Rajaratnam
Feb 20, 2014·Statistics and Its Interface·Zakaria S KhondkerJoseph G Ibrahim

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Citations

Apr 9, 2019·Multivariate Behavioral Research·Donald R WilliamsPhilippe Rast
Jun 18, 2019·The British Journal of Mathematical and Statistical Psychology·Donald R Williams, Philippe Rast
Nov 2, 2019·Multivariate Behavioral Research·Anna C Wysocki, Mijke Rhemtulla

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Methods Mentioned

BETA
flow cytometry

Software Mentioned

glasso
MATLAB
StARS
R package
R gss
R

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