Index: Li 2019 - Graphical Horseshoe Estimator

Li 2019 - Graphical Horseshoe Estimator

Routing Summary

Full capture of Li, Craig and Bhadra (2019), The Graphical Horseshoe Estimator for Inverse Covariance Matrices (arXiv:1707.06661; J. Multivariate Analysis): prior, Gibbs sampler, KL-risk and bias theorems, simulations, gene network.

• Need the paper on one page, PyMC example E19, section map? → Li 2019 - Graphical Horseshoe Estimator - Overview
• Need the prior, conditionals, Algorithm 1, working code? → Li 2019 - Graphical Horseshoe Model and Gibbs Sampler
• Need Thm 3.2 (KL risk) or Thm 4.1 (bias)? → Li 2019 - Kullback-Leibler Risk Bound and Bias Theory
• Need simulation tables and the CEU gene network? → Li 2019 - Simulation Study and Gene Expression Application
• Need G-Wishart, neighbourhood selection, graph posterior? → Bayesian Gaussian Graphical Models - G-Wishart and Neighbourhood Selection

Concept Map

Concept	Note	Type	Depends On	Key Result
GHS prior and sampler	Li 2019 - Graphical Horseshoe Model and Gibbs Sampler	definition	none	closed-form column conditionals preserve PD
KL risk and bias	Li 2019 - Kullback-Leibler Risk Bound and Bias Theory	theorem	prior	$E(Z)=O(1/{\hat{\omega }}^2)$
Simulations, gene data	Li 2019 - Simulation Study and Gene Expression Application	example	theory	best Stein loss in 11/12 settings
G-Wishart etc.	Bayesian Gaussian Graphical Models - G-Wishart and Neighbourhood Selection	concept	GHS	graph-constrained precision priors

Notes

• Li 2019 - Graphical Horseshoe Estimator - Overview — CONTAINS: question, contributions, E19 link, Source Map.
• Li 2019 - Graphical Horseshoe Model and Gibbs Sampler — CONTAINS: GL/BGL/GSCAD, GHS prior, conditionals, PD proof, Python sampler.
• Li 2019 - Kullback-Leibler Risk Bound and Bias Theory — CONTAINS: Lemma 3.1, Thm 3.2, Thm 4.1 with interpretation.
• Li 2019 - Simulation Study and Gene Expression Application — CONTAINS: design, Tables 1 and 3 excerpts, CEU results.
• Bayesian Gaussian Graphical Models - G-Wishart and Neighbourhood Selection — CONTAINS: concept note, no raw source.

Sources

Li 2019 - The Graphical Horseshoe Estimator (arXiv:1707.06661v3).

See Also

Joint Priors and Covariance Matrices | Meinshausen Buhlmann 2010 - Stability Selection - Overview