Torpid Mixing of Simulated Tempering on the Potts Model

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 15, Issue , 2004, Pages 471-480

  Bhatnagar, Nayantara ^a   Randall, Dana ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIMODAL DISTRIBUTIONS; GIBBS DISTRIBUTION; SWAPPING ALGORITHMS;

COMPUTER SIMULATION; FERROMAGNETISM; GRAPH THEORY; MARKOV PROCESSES; MATHEMATICAL MODELS; MONTE CARLO METHODS; PROBABILITY; SAMPLING;

ALGORITHMS;

EID: 1842539531     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (17)

1. C. Borgs, J.T. Chayes, A. Frieze, J.H. Kim, P. Tetali, E. Vigoda, and V.H. Vu. Torpid mixing of some MCMC algorithms in statistical physics. Proc. 40th IEEE Symposium on Foundations of Computer Science, 218-229, 1999.
2. C. Cooper, M.E. Dyer, A.M. Frieze, and R. Rue. Mixing Properties of the Swendsen-Wang Process on the Complete Graph and Narrow Grids. J. Math. Phys. 41: 1499-1527: 2000.
3. P. Diaconis and L. Saloff-Coste. Comparison theorems for reversible Markov chains. Annals of Applied Probability. 3: 696-730, 1993.
4. C.J. Geyer. Markov Chain Monte Carlo Maximum Likelihood. Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface (E.M. Keramidas, ed.), 156-163. Interface Foundation, Fairfax Station, 1991.
5. C.J. Geyer and E.A. Thompson. Annealing Markov Chain Monte Carlo with Applications to Ancestral Inference. J. Amer. Statist. Assoc. 90: 909-920, 1995.
6. V.K. Gore and M.R. Jerrum. The Swendsen-Wang Process Does Not Always Mix Rapidly. J. Statist. Phys. 97: 67-86, 1995.
7. M.R. Jerrum and A.J. Sinclair. Approximate counting, uniform generation and rapidly mixing Markov chains. Information and Computation. 82: 93-133, 1989.
8. S. Kirkpatrick, L. Gellatt Jr., and M. Vecchi. Optimization by simulated annealing. Science. 220: 498-516, 1983.
9. N. Madras and D. Randall. Markov chain decomposition for convergence rate analysis. Annals of Applied Probability. 12: 581-606, 2002.
10. N. Madras and Z. Zheng. On the swapping algorithm. Random Structures and Algorithms. 22: 66-97, 2003.
11. E. Marinari and G. Parisi. Simulated tempering: a new Monte Carlo scheme. Europhys. Lett. 19: 451-458, 1992.
12. R.A. Martin and D. Randall. Sampling adsorbing staircase walks using a new Markov chain decomposition method. Proc. 41st Symposium on the Foundations of Computer Science (FOCS 2000), 492-502, 2000.
13. R.A. Martin and D. Randall. Disjoint decomposition with applications to sampling circuits in some Cayley graphs. Preprint, 2003.
14. N. Metropolis, A. W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller. Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21: 1087-1092, 1953.
15. R.B. Potts. Some Generalized Order-disorder Transformations Proceedings of the Cambridge Philosophical Society, 48: 106-109, 1952.
16. A.J. Sinclair. Algorithms for random generation & counting: a Markov chain approach. Birkhäuser, 1993.
17. Z. Zheng. Analysis of Swapping and Tempering Monte Carlo Algorithms. Dissertation, York Univ., 1999.