Geometric Ergodicity and Hybrid Markov Chains
Open Access
- 1 January 1997
- journal article
- Published by Institute of Mathematical Statistics in Electronic Communications in Probability
- Vol. 2 (none), 13-25
- https://doi.org/10.1214/ecp.v2-981
Abstract
Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will "inherit" the geometric ergodicity of its constituent parts.Keywords
This publication has 19 references indexed in Scilit:
- A note on Metropolis-Hastings kernels for general state spacesThe Annals of Applied Probability, 1998
- Outperforming the Gibbs sampler empirical estimator for nearest-neighbor random fieldsThe Annals of Statistics, 1996
- Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithmsBiometrika, 1996
- Minorization Conditions and Convergence Rates for Markov Chain Monte CarloJournal of the American Statistical Association, 1995
- Computable Bounds for Geometric Convergence Rates of Markov ChainsThe Annals of Applied Probability, 1994
- Sampling-Based Approaches to Calculating Marginal DensitiesJournal of the American Statistical Association, 1990
- Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusionsCommunications in Mathematical Physics, 1986
- Exponential Moments for Hitting Times of Uniformly Ergodic Markov ProcessesThe Annals of Probability, 1983
- Geometric Ergodicity and R-positivity for General Markov ChainsThe Annals of Probability, 1978
- GEOMETRIC ERGODICITY IN DENUMERABLE MARKOV CHAINSThe Quarterly Journal of Mathematics, 1962