On the Geometric Ergodicity of Two-Variable Gibbs Samplers
Statistics Theory
2012-06-22 v1 Statistics Theory
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.
Keywords
Cite
@article{arxiv.1206.4770,
title = {On the Geometric Ergodicity of Two-Variable Gibbs Samplers},
author = {Aixin Tan and Galin L. Jones and James P. Hobert},
journal= {arXiv preprint arXiv:1206.4770},
year = {2012}
}