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

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  • 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.

Suggested Citation

  • Markku Kuismin & Mikko J Sillanpää, 2016. "Use of Wishart Prior and Simple Extensions for Sparse Precision Matrix Estimation," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-20, February.
    • Handle: RePEc:plo:pone00:0148171
    DOI: 10.1371/journal.pone.0148171
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    References listed on IDEAS

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    1. Kubokawa, Tatsuya & Srivastava, Muni S., 2008. "Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1906-1928, October.
    2. Jacob Bien & Robert J. Tibshirani, 2011. "Sparse estimation of a covariance matrix," Biometrika, Biometrika Trust, vol. 98(4), pages 807-820.
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