Book chapter
On the Geometric Ergodicity of Two-Variable Gibbs Samplers
Advances in Modern Statistical Theory and Applications: A Festschrift in honor of Morris L. Eaton
Institute of Mathematical Statistics Collections, 10, Institute of Mathematical Statistics
06/20/2012
DOI: 10.1214/12-IMSCOLL1002
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.
Details
- Title: Subtitle
- On the Geometric Ergodicity of Two-Variable Gibbs Samplers
- Creators
- Aixin Tan - University of IowaGalin L Jones - University of MinnesotaJames P Hobert - University of Florida
- Resource Type
- Book chapter
- Publication Details
- Advances in Modern Statistical Theory and Applications: A Festschrift in honor of Morris L. Eaton
- Publisher
- Institute of Mathematical Statistics
- Series
- Institute of Mathematical Statistics Collections; 10
- DOI
- 10.1214/12-IMSCOLL1002
- Language
- English
- Date published
- 06/20/2012
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257604102771
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