Polynomial convergence rates of Markov chains

Annals of Applied Probability

Volumn 12, Issue 1, 2002, Pages 224-247

  Jarner, Søren F ^a   Roberts, Gareth O ^a  

^a LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Central limit theorems; Foster Liapounov drift conditions; Independence sampler; Markov chains; Polynomial convergence

Indexed keywords

EID: 0036117479     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1015961162     Document Type: Article

References (15)

1. CHUNG, K. L. (1967). Markov Chains with Stationary Transition Probabilities, 2nd ed. Springer, Berlin.
2. DAI, J. and MEYN, S. (1995). Stability and convergence of moments for multiclass queueing networks via fluid limit models. IEEE Trans. Automat. Control 40 1889-1904.
3. FORT, G. and MOULINES, E. (2000). V-subgeometric ergodicity for a Hastings-Metropolis algorithm. Statist. Probab. Lett. 49 401-410.
4. GLYNN, P. and MEYN, S. (1996). A Liapounov bound for solutions of the Poisson equation. Ann. Probab. 24 916-931.
5. MENGERSEN, K. and TWEEDIE, R. (1996). Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist. 24 101-121.
6. MEYN, S. and TWEEDIE, R. (1992). Stability of Markovian processes I: Criteria for discrete-time chains. Adv. in Appl. Probab. 24 542-574.
7. MEYN, S. and TWEEDIE, R. (1993). Markov Chains and Stochastic Stability. Springer, London.
8. NUMMELIN, E. (1984), General Irreducible Markov Chains and Non-Negative Operators. Cambridge Univ. Press.
9. NUMMELIN, E. and TUOMINEN, P. (1982). Geometric ergodicity of Harris recurrent Markov chains with applications to renewal theory. Stochastic Process. Appl. 12 187-202.
10. ROBERTS, G. and ROSENTHAL, J. (2001). Markov chains and de-initialising processes. Scand. J. Statist. 28 489-504.
11. ROBERTS, G. and TWEEDIE, R. (2001). Understanding Markov Chain Monte Carlo. Springer, New York. To appear.
12. SMITH, R. and TIERNEY, L. (1996). Exact transition probabilities for the independence Metropolis sampler. Technical report, Statistical Laboratory, Cambridge Univ. Press.
13. TIERNEY, L. (1994). Markov chains for exploring posterior distributions. Ann. Statist. 22 1701-1762.
14. TUOMINEN, P. and TWEEDIE, R. (1994). Subgeometric rates of convergence of f-ergodic Markov chains. Adv. in Appl. Probab. 26 775-798.
15. TWEEDIE, R. (1983). Criteria for rates of convergence of Markov chains with application to queueing and storage theory. In Probability, Statistics and Analysis (J. F. C. Kingman and G. E. H. Reuter, eds.). Cambridge Univ. Press.