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Bayesian adaptive Lasso estimation of large graphical model based on modified Cholesky decomposition

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  • Li, Fanqun
  • Zhao, Mingtao
  • Zhang, Kongsheng

Abstract

In this paper, based on the modified Cholesky decomposition of the precision matrix, we propose Bayesian adaptive Lasso estimation and maximum adaptive posterior estimation for graphical model. We also recover the graph by minimizing the decoupled shrinkage and selection loss function.

Suggested Citation

  • Li, Fanqun & Zhao, Mingtao & Zhang, Kongsheng, 2024. "Bayesian adaptive Lasso estimation of large graphical model based on modified Cholesky decomposition," Statistics & Probability Letters, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:stapro:v:206:y:2024:i:c:s0167715223002286
    DOI: 10.1016/j.spl.2023.110004
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    References listed on IDEAS

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    1. P. Richard Hahn & Carlos M. Carvalho, 2015. "Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 435-448, March.
    2. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    3. Frederick Wong, 2003. "Efficient estimation of covariance selection models," Biometrika, Biometrika Trust, vol. 90(4), pages 809-830, December.
    4. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    5. Jianhua Z. Huang & Naiping Liu & Mohsen Pourahmadi & Linxu Liu, 2006. "Covariance matrix selection and estimation via penalised normal likelihood," Biometrika, Biometrika Trust, vol. 93(1), pages 85-98, March.
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