%0 Journal Article
%T On the Geometric Ergodicity of Two-Variable Gibbs Samplers
%A Aixin Tan
%A Galin L. Jones
%A James P. Hobert
%J Statistics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1206.4770v1