Statistics and Its Interface

Volume 6 (2013)

Number 2

The Bayesian covariance lasso

Pages: 243 – 259

DOI: https://dx.doi.org/10.4310/SII.2013.v6.n2.a8

Authors

Haitao Chu (Division of Biostatistics, University of Minnesota, Minneapolis, Minn., U.S.A.)

Joseph G. Ibrahim (Department of Biostatistics, University of North Carolina, Chapel Hill, N.C., U.S.A.)

Zakaria S. Khondker (Department of Biostatistics, University of North Carolina, Chapel Hill, N.C., U.S.A.)

Weili Lin (Biomedical Research Imaging Center, University of North Carolina, Chapel Hill, N.C., U.S.A.)

Hongtu Zhu (Department of Biostatistics, University of North Carolina, Chapel Hill, N.C., U.S.A.)

Abstract

Estimation of sparse covariance matrices and their inverse subject to positive definiteness constraints has drawn a lot of attention in recent years. Frequentist methods have utilized penalized likelihood methods, whereas Bayesian approaches rely on matrix decompositions or Wishart priors for shrinkage. In this paper we propose a new method, called the Bayesian Covariance Lasso (BCLASSO), for the shrinkage estimation of a precision (covariance) matrix. We consider a class of priors for the precision matrix that leads to the popular frequentist penalties as special cases, develop a Bayes estimator for the precision matrix, and propose an efficient sampling scheme that does not precalculate boundaries for positive definiteness. The proposed method is permutation invariant and performs shrinkage and estimation simultaneously for non-full rank data. Simulations show that the proposed BCLASSO performs similarly as frequentist methods for non-full rank data.

Keywords

Bayesian covariance lasso, non-full rank data, network exploration, penalized likelihood, precision matrix

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Published 10 May 2013