A Data Driven Bayesian Graphical Ridge Estimator
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Bayesian methodologies prioritising accurate associations above sparsity in Gaussian graphical model (GGM) estimation remain relatively scarce in scientific literature. It is well accepted that the ℓ_2 penalty enjoys a smaller computational footprint in GGM estimation, whilst the ℓ_1 penalty encourages sparsity in the estimand. The Bayesian adaptive graphical lasso prior is used as a departure point in the formulation of a computationally efficient graphical ridge-type prior for events where accurate associations are prioritised over sparse representations. A novel block Gibbs sampler for simulating precision matrices is constructed using a ridge-type penalisation. The Bayesian graphical ridge-type prior is extended to a Bayesian adaptive graphical ridge-type prior. Synthetic experiments indicate that the graphical ridge-type estimators enjoy computational efficiency, in moderate dimensions, and numerical performance, for relatively non-sparse precision matrices, when compared to their lasso counterparts. The adaptive graphical ridge-type estimator is applied to cell signaling data to infer key associations between phosphorylated proteins in human T cell signalling. All computational workloads are carried out using the baygel R package.
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