An analysis of Swendsen-Wang and related sampling methods

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 61, Issue 3, 1999, Pages 623-641

  Fishman, George S ^a,b  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

^b University of North Carolina at Chapel Hill   (United States)

Author keywords

Markov chain Monte Carlo method; Swendsen Wang method

Indexed keywords

EID: 0039425351     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00197     Document Type: Article

References (17)

1. Besag, J. (1974) Spatial interaction and the statistical analysis of lattice systems (with discussion). J. R. Statist. Soc. B, 36, 192-225.
2. Besag, J. and Green, P. J. (1993) Spatial statistics and Bayesian computation. J, R. Statist. Soc. B, 55, 25-37.
3. Devroye, L. (1986) Non-uniform Random Variate Generation. New York: Springer.
4. Edwards, R. G. and Sokal, A. D. (1988) Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation in Monte Carlo. Phys. Rev., 38, 2009-2012.
5. _ _ (1989) Dynamic critical behavior of Wolff's collective mode Monte Carlo algorithm for the two-dimensional O(n) nonlinear σ model. Phys. Rev. D, 40, 1374-1377.
6. Fishman, G. S. (1996a) Convergence bounds for Gibbs and Hastings-Metropolis sampling for several coordinate selection rules. Technical Report TR96/01. Operations Research Department, University of North Carolina, Chapel Hill.
7. _ _ (1996b) Monte Carlo: Concepts, Algorithms, and Applications. New York: Springer.
8. Gray, A. J. (1994) Simulating posterior Gibbs distributions: a comparison of the Swendsen-Wang and Gibbs sampler methods. Statist. Comput., 4, 189-201.
9. Grimmett, G. (1993) Random graphical networks. In Networks and Chaos - Statistical and Probabilistic Aspects (eds O. E. Barndorff-Nielsen, J. L. Jensen and W. S. Kendall). London: Chapman and Hall.
10. Kandel, D., Domany, E. and Brandt, A. (1989) Simulations without critical slow down: Ising and three-state Potts models. Phys. Rev. B, 40, 330-340.
11. Kandel, D., Domany, E., Ron, D., Brandt, A. and Loh, Jr, E. (1988) Simulations without critical slow down. Phys. Rev. Lett., 60, 1591-1594.
12. Klein, W., Ray, T. and Tamayo, P. (1989) Scaling ansatz for Swendsen-Wang dynamics. Phys. Rev. Lett., 62, 163-166.
13. Roberts, G. O. and Rosenthal, J. S. (1999) Convergence of slice sampler Markov chains. J. R. Statist. Soc. B, 61, 643-660.
14. Swendsen, R. H. and Wang, J.-S. (1987) Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett., 58, 86-88.
15. Tamayo, P., Brower, R. C. and Klein, W. (1990) Single-cluster Monte Carlo dynamics for the Ising model. J. Statist. Phys., 58, 1083-1094.
16. Wilkinson, J. H. (1965) The Algebraic Eigenvalue Problem. Oxford: Clarendon.
17. Wolff, U. (1989) Collective Monte Carlo updating for spin systems. Phys. Rev. Lett., 62, 361-364.