On the applicability of regenerative simulation in Markov chain Monte Carlo

Biometrika

Volumn 89, Issue 4, 2002, Pages 731-743

  Hobert, James P ^a   Jones, Galin L ^b   Presnell, Brett ^a   Rosenthal, Jeffrey S ^c  

^a University of Florida   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

Asymptotic standard error; Burn in; Central limit theorem; Geometric ergodicity; Minorisation condition; Slice sampler

Indexed keywords

EID: 2142780945     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/89.4.731     Document Type: Article

References (36)

1. ATHREYA, K. B. & NEY, P. (1978). A new approach to the limit theory of recurrent Markov chains. Trans. Am. Math. Soc. 245, 493-501.
2. BRATLEY, P., Fox, B. L. & SCHRAGE, L. E. (1987). A Guide to Simulation, 2nd ed. New York: Springer-Verlag.
3. CHAN, K. S. (1993). On the central limit theorem for an ergodic Markov chain. Stock. Proces. Applic. 47, 113-7.
4. CHAN, K. S. & GEYER, C. J. (1994). Comment on 'Markov chains for exploring posterior distributions' by L. Tierney. Ann. Statist. 22, 1747-58.
5. DAMIEN, P., WAKEFIELD, J. & WALKER, S. (1999). Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables. J. R. Statist. Soc. B 61, 331-41.
6. FORT, G. & MOULINES, E. (2000). V-Subgeometric ergodicity for a Hastings-Metropolis algorithm. Statist. Prob. Lett. 49, 401-10.
7. GEYER, C. J. (1992). Practical Markov chain Monte Carlo (with Discussion). Statist. Sci. 7, 473-511.
8. GEYER, C. J. & THOMPSON, E. A. (1995). Annealing Markov chain Monte Carlo with applications to ancestral inference. J. Am. Statist. Assoc. 90, 909-20.
9. GILKS, W. R., ROBERTS, G. O. & SAHU, S. K. (1998). Adaptive Markov chain Monte Carlo through regeneration. J. Am. Statist. Assoc. 93, 1045-54.
10. HOBERT, J. P. & GEYER, C. J. (1998). Geometric ergodicity of Gibbs and block Gibbs samplers for a hierarchical random effects model. J. Mult. Anal. 67, 414-30.
11. JARNER, S. F. & HANSEN, E. (2000). Geometric ergodicity of Metropolis algorithms. Stock. Proces. Applic. 85, 341-61.
12. JARNER, S. F. & ROBERTS, G. O. (2002). Polynomial convergence rates of Markov chains. Ann. Appl. Prob. 12, 224-47.
13. JONES, G. L. & HOBERT, J. P. (2001). Honest exploration of intractable probability distributions via Markov chain Monte Carlo. Statist. Sci. 16, 312-34.
14. KIPNIS, C. & VARADHAN, S. R. S. (1986). Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Commun. Math. Phys. 104, 1-19.
15. MENGERSEN, K. & TWEEDIE, R. L. (1996). Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist. 24, 101-21.
16. MEYN, S. P. & TWEEDIE, R. L. (1993). Markov Chains and Stochastic Stability. London: Springer-Verlag.
17. MEYN, S. P. & TWEEDIE, R. L. (1994). Computable bounds for geometric convergence rates of Markov chains. Ann. Appl. Prob. 4, 981-1011.
18. MIRA, A. & TIERNEY, L. (2001). Efficiency and convergence properties of slice samplers. Scand. J. Statist. 29, 1035-53.
19. MYKLAND, P., TIERNEY, L. & Yu, B. (1995). Regeneration in Markov chain samplers. J. Am. Statist. Assoc. 90, 233-41.
20. NEAL, R. M. (2003). Slice sampling. Ann. Statist. To appear.
21. NUMMELIN, E. (1978). A splitting technique for Harris recurrent Markov chains. Z. Wahr. Verw. Geb. 43, 309-18.
22. NUMMELIN, E. (1984). General Irreducible Markov Chains and Non-negative Operators. London: Cambridge University Press.
23. NUMMELIN, E. & TUOMINEN, P. (1982). Geometric ergodicity of Harris recurrent Markov chains with applications to renewal theory. Stoch. Proces. Applic. 12, 187-202.
24. NUMMELIN, E. & TUOMINEN, P. (1983). The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewal theory. Stoch. Proces. Applic. 15, 295-311.
25. PRIESTLEY, M. B. (1981). Spectral Analysis and Time Series. London: Academic.
26. RIPLEY, B. D. (1987). Stochastic Simulation. New York: John Wiley and Sons.
27. ROBERT, C. P. (1995). Convergence control methods for Markov chain Monte Carlo algorithms. Statist. Sci. 10, 231-53.
28. ROBERT, C. P. & CASELLA, G. (1999). Monte Carlo Statistical Methods. New York: Springer.
29. ROBERTS, G. O. & ROSENTHAL, J. S. (1997). Geometric ergodicity and hybrid Markov chains. Electron. Commun. Prob. 2, 13-25.
30. ROBERTS, G. O. & ROSENTHAL, J. S. (1998a). Markov chain Monte Carlo: Some practical implications of theoretical results (with Discussion). Can. J. Statist. 26, 5-31.
31. ROBERTS, G. O. & ROSENTHAL, J. S. (1998b). On convergence rates of Gibbs samplers for uniform distributions. Ann. Appl. Prob. 8, 1291-302.
32. ROBERTS, G. O. & ROSENTHAL, J. S. (1999). Convergence of slice sampler Markov chains. J. R. Statist. Soc. B 61, 643-60.
33. ROBERTS, G. O. & ROSENTHAL, J. S. (2001). Markov chains and de-initializing processes. Scand. J. Statist. 28, 489-504.
34. ROBERTS, G. O. & TWEEDIE, R. L. (1996). Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika 83, 95-110.
35. ROSENTHAL, J. S. (1995). Minorization conditions and convergence rates for Markov chain Monte Carlo. J. Am. Statist. Assoc. 90, 558-66.
36. TUOMINEN, P. & TWEEDIE, R. L. (1994). Subgeometric rates of convergence f-ergodic Markov chains. Adv. Appl. Prob. 26, 775-798.