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Abstract:
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For various Bayesian penalized regression models, we show that the corresponding 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 ensuring reliable Bayesian computation. Our results allow us to also provide default starting values for the Gibbs samplers.
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