On convergence rates of Gibbs samplers for uniform distributions

Annals of Applied Probability

Volumn 8, Issue 4, 1998, Pages 1291-1302

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

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

Curvature; Gibbs sampler; Markov chain; Monte Carlo; Slice sampler; Uniform distribution

Indexed keywords

EID: 0032280918     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1028903381     Document Type: Article

References (14)

1. BAÑUELOS, R. and CARROLL, T. (1994). Brownian motion and the fundamental frequency of a drum. Duke Math. J. 75 575-602.
2. BÉLISLE, C. (1997). Slow convergence of the Gibbs sampler. Technical Report 172, Dept. Statistics, Univ. British Columbia. Available at http://www.stats.bris.ac.uk/MCMC/.
3. DAMIEN, P., WAKEFIELD, J. C. and WALKER, S. (1997). Gibbs sampling for Bayesian nonconjugate and hierarchical models using auxiliary variables. Imperial College, London. Preprint.
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. HIGDON, D. M. (1997). Auxiliary variable methods for Markov chain Monte Carlo with applications. Preprint, Statistics and Decision Sciences, Duke Univ. Available at http://www.stats.bris.ac.uk/MCMC/.
6. 2 spectrum for Markov chains and Markov processes: a generalization of Cheeger's inequality. Trans. Amer. Math. Soc. 309 557-580.
7. MEYN, S. P. and TWEEDIE, R. L. (1993). Markov Chains and Stochastic Stability. Springer, New York.
8. MIRA, A. and TIERNEY, L. (1997). On the use of auxiliary variables in Markov chain Monte Carlo sampling. School of Statistics, Univ. Minnesota. Unpublished manuscript.
9. NUMMELIN, E. (1984). General Irreducible Markov Chains and Non-negative Operators. Cambridge Univ. Press.
10. ROBERTS, G. O. and ROSENTHAL, J. S. (1997a). Geometric ergodicity and hybrid Markov chains. Elec. Comm. Prob. 2 13-25.
11. ROBERTS, G. O. and ROSENTHAL, J. S. (1997b). Convergence of slice sampler Markov chains. Unpublished manuscript.
12. ROBERTS, G. O. and TWEEDIE, R. L. (1996). Geometric convergence and central limit theorems for multidimensional-Hastings Metropolis algorithms. Biometrika 83 96-110.
13. 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.
14. TIERNEY, L. (1994). Markov chains for exploring posterior distributions (with discussion). Ann. Statist. 22 1701-1762.