The wang-landau algorithm in general state spaces: applications and convergence analysis

Statistica Sinica

Volumn 20, Issue 1, 2010, Pages 209-233

  Atchadé, Yves F ^a   Liu, Jun S ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

Adaptive mcmc; Geometric ergodicity; Monte carlo methods; Multicanonical sampling; Stochastic approximation; Trans dimensional mcmc; Wang landau algorithm

Indexed keywords

EID: 77949412635     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. Andrieu, C and Atchade, Y. F. (2007). On the efficiency of adaptive MCMC algorithms. Electron. Comm. Probab. 12, 336-349.
2. Andrieu, C. and Robert, C P. (2001). Controlled MCMC for optimal sampling. Technical report, Université Paris Dauphine, Ceremade 0125.
3. Andrieu, C. and Moulines, E. (2006). On the ergodicity properties of some adaptive MCMC algorithms. Ann. Appl. Probab. 16, 1462-1505.
4. Andrieu, C., Moulines, E. and Priouret, P. (2005). Stability of stochastic approximation under verifiable conditions. SIAM J. Control Optim. 44, 283-312 (electronic).
5. Atchadé, Y. F. and Liu, J. S. (2006). Discussion of "Equi-energy sampler" by Kou, Zhou and Wong. Ann. Statist. 34, 1620-1628.
6. Atchadé, Y. F. and Rosenthal, J. S. (2005). On adaptive Markov Chain Monte Carlo algorithm. Bernoulli 11, 815-828.
7. Baxendale, P. H. (2005). Renewal theory and computable convergence rates for geometrically ergodic Markov chains. Ann. Appl. Probab. 15, 700-738.
8. Benveniste, A., Métivier, M. and Priouret, P. (1990). Adaptive Algorithms and Stochastic approximations. Applications of Mathematics. Springer, Paris-New York,
9. Berg, B. A. and Neuhaus, T. (1992). Multicanonical ensemble: A new approach to simulate first-order phase transitions. Phys. Rev. Lett. 68,
10. Brockwell, A. E. and Kadaně, J. B. (2005). Identification of regeneration times in MCMC simulation, with application to adaptive schemes. J. Comput. Graph. Statist. 14, 436-458.
11. Delyon, B. (1996). General results on the convergence of stochastic algorithms. IEEE Trans. Automat. Control 41, 1245-1255.
12. Geyer, C J. and Thompson, E. A. (1995). Annealing Markov Chain Monte Carlo with applications to pedigree analysis. J. Amer. Statist. Assoc. 90, 909-920.
13. Gilks, W. R., Roberts, G. O. and Sahu, S. K. (1998). Adaptive Markov Chain Monte Carlo through regeneration. J. Amer. Statist. Assoc. 93, 1045-1054.
14. Green, P. J. (1995). Reversible jump Markov Chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711-732.
15. Haario, H., Sakesman, E. and Tamminen, J. (2001). An adaptive Metropolis algorithm. Bernoulli 7, 223-242.
16. Liang, F. and Wong, W. H. (2001). Real-parameter evolutionary Monte Carlo with applications to Bayesian mixture models. J. Amer. Statist. Assoc. 96, 653-666.
17. Liang, F., Liu, C and Carroll, R. J. (2007). Stochastic approximation in Monte Carlo computation. J. Amer. Statist. Assoc. 102, 305-320.
18. Marinari, E. and Parisi, G. (1992). Simulated tempering: A new Monte Carlo schemes. Europhys. Lett. 19, 451-458.
19. Mira, A. and Sargent, D. J. (2003). A new strategy for speeding Markov Chain Monte Carlo algorithms. Stat. Methods Appl. 12, 49-60.
20. Rosenthal, J. S. and Roberts, G. O. (2007). Coupling and ergodicity of adaptive MCMC J. Appl. Probab. 44, 458-475.
21. Wang, F. and Landau, D. P. (2001). Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett. 86, 2050-2053.