On the Geometric Ergodicity of Two-variable Gibbs Samplers
نویسندگان
چکیده
A Markov chain is geometrically ergodic if it converges to its invariant distribution at a geometric rate in total variation norm. We study geometric 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 simultaneously 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. ∗Research supported by the National Science Foundation and the National Institutes for Health. †Research supported by the National Science Foundation.
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