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2017 Geometric ergodicity of Gibbs samplers in Bayesian penalized regression models
Dootika Vats
Electron. J. Statist. 11(2): 4033-4064 (2017). DOI: 10.1214/17-EJS1351

Abstract

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.

Citation

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Dootika Vats. "Geometric ergodicity of Gibbs samplers in Bayesian penalized regression models." Electron. J. Statist. 11 (2) 4033 - 4064, 2017. https://doi.org/10.1214/17-EJS1351

Information

Received: 1 September 2016; Published: 2017
First available in Project Euclid: 19 October 2017

zbMATH: 1374.60127
MathSciNet: MR3714307
Digital Object Identifier: 10.1214/17-EJS1351

Subjects:
Primary: 60J05
Secondary: 62F15

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Vol.11 • No. 2 • 2017
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