Abstract
We generalize and simplify a result of Schervish and Carlin (1992) concerning the convergence of Markov chains to their stationary distributions. We prove geometric convergence for any Markov chain whose transition operator is compact and has everywhere-positive density functions (with respect to some reference measure). We also provide, without requiring compactness, a quantitative estimate of the convergence rate, given in terms of the stationary distribution.
Original language | English (US) |
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Pages (from-to) | 333-338 |
Number of pages | 6 |
Journal | Statistics and Probability Letters |
Volume | 22 |
Issue number | 4 |
DOIs | |
State | Published - Mar 1995 |
Bibliographical note
Funding Information:We thank Peter gosenthal for helpful discussions, and thank the referee for useful comments. This work was partially supported by NSF and by NSERC.
Keywords
- Compact operator
- Geometric convergence
- Gibbs sampler
- Hilbert-Schmidt condition
- Markov chain
- Monte Carlo
- Stationary distribution