Geometric ergodicity of the Bayesian Lasso

DOI10.1214/13-EJS841zbMath1349.60124OpenAlexW2104863866MaRDI QIDQ367204

Kshitij Khare, James P. Hobert

Publication date: 26 September 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ejs/1378817879

zbMATH Keywords

Markov chainconvergence rateBayesian lassogeometric drift condition

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Ridge regression; shrinkage estimators (Lasso) (62J07) Central limit and other weak theorems (60F05) Bayesian inference (62F15)

Related Items

Bayesian bridge regression, Approximate Gibbs sampler for Bayesian Huberized lasso, Geometric ergodicity of Gibbs samplers for the horseshoe and its regularized variants, Convergence rates of two-component MCMC samplers, Assessing and Visualizing Simultaneous Simulation Error, Unnamed Item, Estimating accuracy of the MCMC variance estimator: asymptotic normality for batch means estimators, Bayesian Approaches to Shrinkage and Sparse Estimation, Complexity results for MCMC derived from quantitative bounds, Asynchronous and Distributed Data Augmentation for Massive Data Settings, Geometric ergodicity for Bayesian shrinkage models, Bayesian MIDAS penalized regressions: estimation, selection, and prediction, Uncertainty Quantification for Modern High-Dimensional Regression via Scalable Bayesian Methods

Cites Work

• Unnamed Item
• Sub-optimality of some continuous shrinkage priors
• A new proof of convergence of MCMC via the ergodic theorem
• Markov chains and stochastic stability
• Markov chain Monte Carlo: can we trust the third significant figure?
• General state space Markov chains and MCMC algorithms
• Batch means and spectral variance estimators in Markov chain Monte Carlo
• Inference with normal-gamma prior distributions in regression problems
• Penalized regression, standard errors, and Bayesian Lassos
• Fixed-Width Output Analysis for Markov Chain Monte Carlo
• The horseshoe estimator for sparse signals
• The Bayesian Lasso
• Markov-chain monte carlo: Some practical implications of theoretical results
• Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo
• Efficient Empirical Bayes Variable Selection and Estimation in Linear Models