Two convergence properties of hybrid samplers

Annals of Applied Probability

Volumn 8, Issue 2, 1998, Pages 397-407

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

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

Convergence rate; Geometric convergence; Hybrid sampler; Markov chain; Monte Carlo

Indexed keywords

EID: 0032221199     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1028903533     Document Type: Article

References (16)

1. ALDOUS, D. and DIACONIS, P. (1987). Strong stopping times and finite random walks. Adv. in Appl. Math. 8 69-97.
2. BOOTHBY, W. M. (1986). An Introduction to Differentiable Manifolds and Riemannian Geometry. Academic Press, Orlando, FL.
3. CHAN, K. S. and GEYE, C. J. (1994). Discussion of "Markov chains for exploring posterior distributions" by L. Tierney. Ann. Statist. 22 1747-1758.
4. GELFAND, A. E. and SMITH, A. F. M. (1990). Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398-409.
5. GREEN, P. J. (1994). Reversible jump MCMC computation and Bayesian model determination. Technical report, Dept. Mathematics, Univ. Bristol.
6. HASTINGS, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 97-109.
7. METROPOLIS, N., ROSENBLUTH, A., ROSENBLUTH, M., TELLER, A. and TELLER, E. (1953). Equations of state calculations by fast computing machines. J. Chem. Phys. 21 1087-1091.
8. MEYN, S. P. and TWEEDIE, R. L. (1993). Markov Chains and Stochastic Stability. Springer, London.
9. MEYN, S. P. and TWEEDIE, R. L. (1994). Computable bounds for convergence rates of Markov chains. Ann. Appl. Probab. 4 981-1011.
10. NUMMELIN, E. (1984). General Irreducible Markov Chains and Non-Negative Operators. Cambridge Univ. Press.
11. ROBERTS, G. O. and ROSENTHAL, J. S. (1997). Geometric ergodicity and hybrid Markov chains. Electronic Communications in Probability 2 13-25.
12. ROBERTS, G. O. and TWEEDIE, R. L. (1996). Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika 83 95-110.
13. ROSENTHAL, J. S. (1995). Minorization conditions and convergence rates for Markov chain Monte Carlo. J. Amer. Statist. Assoc. 90 558-566.
14. SMITH, A. F. M. and ROBERTS, G. O. (1993). Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (with discussion). J. Roy. Statist. Soc. Ser. B 55 3-24.
15. TIERNEY, L. (1994). Markov chains for exploring posterior distributions (with discussion). Ann. Statist. 22 1701-1762.
16. TIERNEY, L. (1995). A note on Metropolis-Hastings kernels for general state spaces. Technical Report 606, School of Statistics, Univ. Minnesota.