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High-Dimensional Bayesian Regularised Regression with the BayesReg Package
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abstract
Bayesian penalized regression techniques, such as the Bayesian lasso and the Bayesian horseshoe estimator, have recently received a significant amount of attention in the statistics literature. However, software implementing state-of-the-art Bayesian penalized regression, outside of general purpose Markov chain Monte Carlo platforms such as STAN, is relatively rare. This paper introduces bayesreg, a new toolbox for fitting Bayesian penalized regression models with continuous shrinkage prior densities. The toolbox features Bayesian linear regression with Gaussian or heavy-tailed error models and Bayesian logistic regression with ridge, lasso, horseshoe and horseshoe$+$ estimators. The toolbox is free, open-source and available for use with the MATLAB and R numerical platforms.
Forward citations
Cited by 4 Pith papers
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New Gibbs samplers for robust median regression with horseshoe, horseshoe+, and regularized horseshoe priors; simulations show the first two yield near-95% credible intervals in high dimensions even without exact sparsity.
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Efficient Parameter Estimation for Bayesian Network Classifiers using Hierarchical Linear Smoothing
Hierarchical linear smoothing replaces expensive HDP Gibbs sampling in Bayesian network classifiers with a fast log-linear regression that achieves comparable or better accuracy.
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The Lasso Distribution: Properties, Sampling Methods, and Applications in Bayesian Lasso Regression
The authors define the Lasso distribution, derive its properties including an inverse-CDF sampler, and use it to build a faster Bayesian lasso Gibbs sampler in the BayesianLasso R package.
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