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arXiv · 1206.4770

On the Geometric Ergodicity of Two-Variable Gibbs Samplers

Aixin Tan·Galin L. Jones·James P. Hobert
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Abstract

A Markov chain is geometrically ergodic if it converges to its in- variant distribution at a geometric rate in total variation norm. We study geo- metric ergodicity of deterministic and random scan versions of the two-variable Gibbs sampler. We give a sufficient condition which simultaneously guarantees both versions are geometrically ergodic. We also develop a method for simul- taneously establishing that both versions are subgeometrically ergodic. These general results allow us to characterize the convergence rate of two-variable Gibbs samplers in a particular family of discrete bivariate distributions.

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Aixin Tan, Galin L. Jones, James P. Hobert. 2012-06-21. On the Geometric Ergodicity of Two-Variable Gibbs Samplers. https://arxiv.org/abs/1206.4770

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