Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms

Journal of Applied Probability

Volumn 44, Issue 2, 2007, Pages 458-475

  Roberts, Gareth O ^a,c   Rosenthal, Jeffrey S ^b  

^a LANCASTER UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF TORONTO   (Canada)

^c LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Computational methods; Markov chains

Indexed keywords

EID: 34548026526     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1183667414     Document Type: Article

References (30)

1. ANDRIEU, C. AND MOULINES, E. (2006). On the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms. Ann. Appl. Prob. 16, 1462-1505.
2. ANDRIEU, C. AND ROBERT, C. P. (2002). Controlled MCMC for optimal sampling. Preprint.
3. ATCHADÉ, Y. F. AND ROSENTHAL, J. S. (2005). On adaptive Markov chain Monte Carlo algorithms. Bernoulli 11, 815-828.
4. BAXENDALE, P. H. (2005). Renewal theory and computable convergence rates for geometrically ergodic Markov chains. Ann. Appl. Prob. 15, 700-738.
5. BÉDARD, M. (2006). On the robustness of optimal scaling for Metropolis-Hastings algorithms. Doctoral Thesis, University of Toronto.
6. BROCKWELL, A. E. AND KADANE, J. B. (2005). Identification of regeneration times in MCMC simulation, with application to adaptive schemes. J. Comput. Graph. Statist. 14, 436-458.
7. FORT, G. AND MOULINES, E. (2000). Computable bounds for subgeometrical and geometrical ergodicity. Preprint. Available at http://citeseer.ist.psu.edu/fort00computable.html.
8. FORT, G. AND MOULINES, E. (2003). Polynomial ergodicity of Markov transition kernels. Stoch. Process. Appl. 103, 57-99.
9. FRISTEDT, B. AND GRAY, L. (1997). A Modern Approach to Probability Theory. Birkhäuser, Boston, MA.
10. GILKS, W. R., ROBERTS, G. O. AND SAHU, S. K. (1998). Adaptive Markov chain Monte Carlo. J. Amer. Statist. Assoc. 93, 1045-1054.
11. HAARIO, H., SAKSMAN, E. AND TAMMINEN, J. (2001). An adaptive Metropolis algorithm. Bernoulli 7, 223-242.
12. HÄGGSTRÖM, O. (2001). A note on disagreement percolation. Random Structures Algorithms 18, 267-278.
13. JARNER, S. F. AND ROBERTS, G. O. (2002). Polynomial convergence rates of Markov chains. Ann. Appl. Prob. 12, 224-247.
14. MEYN, S. P. AND TWEEDIE, R. L. (1993). Markov Chains and Stochastic Stability. Springer, London.
15. MEYN, S. P. AND TWEEDIE, R. L. (1994). Computable bounds for convergence rates of Markov chains. Ann, Appl. Prob. 4, 981-1011.
16. PASARICA, C. AND GELMAN, A. (2003). Adaptively scaling the Metropolis algorithm using the average squared jumped distance. Preprint.
17. r. Stoch. Process. Appl. 82, 143-155.
18. ROBBINS, H. AND MONRO, S. (1951). A stochastic approximation method. Ann. Math. Statist. 22, 400-407.
19. ROBERTS, G. O. AND ROSENTHAL, J. S. (2001). Optimal scaling for various Metropolis-Hastings algorithms. Statist. Sci. 16, 351-367.
20. ROBERTS, G. O. AND ROSENTHAL, J. S. (2002). One-shot coupling for certain stochastic recursive sequences. Stoch. Process. Appl. 99, 195-208.
21. ROBERTS, G. O. AND ROSENTHAL, J. S. (2004). General state space Markov chains and MCMC algorithms. Prob. Surveys 1, 20-71.
22. ROBERTS, G. O. AND TWEEDIE, R. L. (1999). Bounds on regeneration times and convergence rates for Markov chains. Stoch. Process. Appl. 80, 211-229. (Correction: 91 (2001), 337-338.)
23. ROBERTS, G. O., GELMAN, A. AND GILKS, W. R. (1997). Weak convergence and optimal scaling of random walk Metropolis algorithms. Ann. Appl. Prob. 7, 110-120.
24. ROBERTS. G. O., ROSENTHAL, J. S. AND SCHWARTZ, P. O. (1998). Convergence properties of perturbed Markov chains. J. Appl. Prob.35, 1-11.
25. ROSENTHAL, J. S. (1995). Minorization conditions and convergence rates for Markov chain Monte Carlo. J. Amer. Statist. Assoc. 90, 558-566.
26. ROSENTHAL, J. S. (1997). Faithful couplings of Markov chains: now equals forever. Adv. Appl. Math. 18, 372-381.
27. ROSENTHAL, J. S. (2000). A First Look at Rigorous Probability Theory. World Scientific, Singapore.
28. ROSENTHAL, J. S. (2002). Quantitative convergence rates of Markov chains: a simple account. Electron. Commun. Prob. 7, 123-128.
29. ROSENTHAL, J. S. (2004). Adaptive MCMC Java applet. Available at http://probability.ca/jeff/java/adapt.html.
30. TIERNEY, L. (1994). Markov chains for exploring posterior distributions (with discussion). Ann. Statist. 22, 1701-1762.