Slow convergence of the Gibbs sampler

Canadian Journal of Statistics

Volumn 26, Issue 4, 1998, Pages 629-641

  Bélisle, Claude ^a  

^a UNIVERSITÉ LAVAL   (Canada)

Author keywords

Geometric ergodicity; Gibbs sampler; Hit and run sampler; Markov chain Monte Carlo methods

Indexed keywords

EID: 0032216915     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3315722     Document Type: Article

References (18)

1. Athreya, K.B., Doss, H., and Sethuraman, J. (1996). On the convergence of the Markov chain simulation method. Ann. Statist., 24, 69-100.
2. Bélisle, C., Romeijn, H.E., and Smith, R.L. (1993). Hit-and-run algorithms for generating multivariate distributions. Math. Oper. Res., 18, 255-266.
3. Bélisle, C., Boneh, A., and Caron. R.J. (1998). Convergence properties of hit-and-run samplers. Stochastic Models, 14(4), 767-800.
4. Berbee, H.C.P., Boender, C.G.E., Rinnooy Kan, A.H.G., Scheffer, C.L., Smith, R.L., and Teigen, J. (1987). Hit-and-run algorithms for the identification of nonredundant linear inequalities. Math. Programming, 37, 184-207.
5. Chan, K.S. (1993). Asymptotic behavior of the Gibbs sampler. J. Amer. Statist. Assoc., 88, 320-326.
6. Chen, M.-H., and Schmeiser, B.W. (1993). Performance of the Gibbs, hit-and-run, and Metropolis samplers. J. Comput. Graph. Statist., 2, 251-272.
7. Chen, M.-H., and Schmeiser, B.W. (1996). General hit-and-run Monte Carlo sampling for evaluating multidimensional integrals. Oper. Res. Lett., 19, 161-169.
8. Gelfand, A.E., and Smith, A.P.M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc., 85, 398-409.
9. Liu, J.S., Wong, W.H., and Kong, A. (1995). Covariance structure and convergence rate of the Gibbs sampler with various scans. J. Roy. Statist. Sac. Ser. B, 57, 157-169.
10. Mengersen, K.L., and Tweedie, R.L. (1996). Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist., 24, 101-121.
11. Nummelin, E. (1984). General Irreducible Markov Chains and Non-negative Operators. Cambridge Univ. Press, Cambridge.
12. Orey, S. (1971). Limit Theorems for Markov Chain Transition Probabilities. Van Nostrand Reinhold, New York.
13. Revuz, D. (1975). Markov Chains. North-Holland. Amsterdam.
14. Roberts, G.O., and Poison, N.G. (1994). On the geometric convergence of the Gibbs sampler. J. Roy. Statist. Soc. Ser. B. 56, 377-384.
15. Roberts. G.O., and Rosenthal, J.S. (1997). On convergence rates of Gibbs samplers for uniform distributions. Technical Report. Department of Statistics, University of Toronto. To appear in Ann. Appl. Probab.
16. Schervish, M.J., and Carlin, B.P. (1992). On the convergence of successive substitution sampling. J. Comput. Graph. Statist., 1, 111-127.
17. Tiemey, L. (1994). Markov chains for exploring posterior distributions. Ann. Statist., 22, 1701-1762.
18. Zabinsky, Z.B., Smith, R.L., McDonald, J.F., Romeijn, H.E., and Kaufman, D.E. (1993). Improving hit-and-run for global optimization. J. Global Optim., 3, 171-192.