Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 11, Number 2 (2017), 4033-4064.
Geometric ergodicity of Gibbs samplers in Bayesian penalized regression models
We consider three Bayesian penalized regression models and show that the respective deterministic scan Gibbs samplers are geometrically ergodic regardless of the dimension of the regression problem. We prove geometric ergodicity of the Gibbs samplers for the Bayesian fused lasso, the Bayesian group lasso, and the Bayesian sparse group lasso. Geometric ergodicity along with a moment condition results in the existence of a Markov chain central limit theorem for Monte Carlo averages and ensures reliable output analysis. Our results of geometric ergodicity allow us to also provide default starting values for the Gibbs samplers.
Electron. J. Statist., Volume 11, Number 2 (2017), 4033-4064.
Received: September 2016
First available in Project Euclid: 19 October 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 62F15: Bayesian inference
Vats, Dootika. Geometric ergodicity of Gibbs samplers in Bayesian penalized regression models. Electron. J. Statist. 11 (2017), no. 2, 4033--4064. doi:10.1214/17-EJS1351. https://projecteuclid.org/euclid.ejs/1508378637