Towards optimal scaling of metropolis-coupled Markov chain Monte Carlo

Statistics and Computing

Volumn 21, Issue 4, 2011, Pages 555-568

  Atchadé, Yves F ^a   Roberts, Gareth O ^b   Rosenthal, Jeffrey S ^c  

^a UNIVERSITY OF MICHIGAN   (United States)

^b UNIVERSITY OF WARWICK   (United Kingdom)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

Metropolis coupled MCMC; Optimal scaling; Simulated tempering

Indexed keywords

EID: 80051470705     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-010-9192-1     Document Type: Article

References (31)

1. Andrieu, C., Moulines, E.: On the ergodicity properties of some Markov chain Monte Carlo algorithms. Ann. Appl. Probab. 44(2), 458-475 (2007).
2. Andrieu, C., Robert, C. P.: Controlled MCMC for optimal sampling. Preprint (2001).
3. Atchade, Y. F.: An adaptive version of the Metropolis adjusted Langevin algorithm with a truncated drift. Methodol. Comput. Appl. Probab. 8(2), 235-254 (2006).
4. Atchade, Y. F., Liu, J. S.: The Wang-Landau algorithm in general state spaces: applications and convergence analysis. Stat. Sin. 20, 209-233 (2010).
5. Cooke, B., Schmidler, S. C.: Preserving the Boltzmann ensemble in replica-exchange molecular dynamics. J. Chem. Phys. 129, 164112 (2008).
6. Delmas, J.-F., Jourdain, B.: Does waste recycling really improve the multi-proposal Metropolis-Hastings algorithm? An analysis based on control variates. J. Appl. Probab. 46(4), 938-959 (2009).
7. Earl, D. J., Deem, M. W.: Parallel tempering: theory, applications, and new perspectives. J. Phys. Chem. B 108, 6844 (2005).
8. Frenkel, D.: Waste-recycling Monte Carlo. In: Computer Simulations in Condensed Matter: From Materials to Chemical Biology. Lecture Notes in Physics, vol. 703. Springer, Berlin (2006).
9. Geyer, C. J.: Markov chain Monte Carlo maximum likelihood. In: Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, pp. 156-163 (1991).
10. Glynn, P. W., Heidelberger, P.: Analysis of parallel, replicated simulations under a completion time constraint. ACM Trans. Model. Simul. 1, 3-23 (1991).
11. Green, P. J., Mira, A.: Delayed rejection in reversible jump Metropolis-Hastings. Biometrika 88(3), 1035-1053 (2001).
12. Hastings, W. K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109 (1970).
13. Iba, Y.: Extended ensemble Monte Carlo. Int. J. Mod. Phys. C 12(5), 623-656 (2001).
14. Kofke, D. A.: On the acceptance probability of replica-exchange Monte Carlo trials. J. Chem. Phys. 117, 6911 (2002). Erratum: J. Chem. Phys. 120, 10852.
15. Kofke, D. A.: Comment on "the incomplete beta function law for parallel tempering sampling of classical canonical systems". J. Chem. Phys. 121, 1167 (2004).
16. Kone, A., Kofke, D. A.: Selection of temperature intervals for parallel-tempering simulations. J. Chem. Phys. 122, 206101 (2005).
17. Lee, A., Yau, C., Giles, M. B., Doucet, A., Holmes, C. C.: On the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo Methods. Preprint (2009).
18. Madras, N., Zheng, Z.: On the swapping algorithm. Random Struct. Algorithms 22, 66-97 (2003).
19. Marinari, E., Parisi, G.: Simulated tempering: a new Monte Carlo scheme. Europhys. Lett. 19, 451-458 (1992).
20. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., Teller, E.: Equations of state calculations by fast computing machines. J. Chem. Phys. 21, 1087-1091 (1953).
21. Predescu, C., Predescu, M., Ciobanu, C. V.: The incomplete beta function law for parallel tempering sampling of classical canonical systems. J. Chem. Phys. 120, 4119 (2004).
22. Robbins, H., Monro, S.: A stochastic approximation method. Ann. Math. Stat. 22, 400-407 (1951).
23. Roberts, G. O., Gelman, A., Gilks, W. R.: Weak convergence and optimal scaling of random walk Metropolis algorithms. Ann. Appl. Probab. 7, 110-120 (1997).
24. Roberts, G. O., Rosenthal, J. S.: Optimal scaling of discrete approximations to Langevin diffusions. J. R. Stat. Soc. B 60, 255-268 (1998).
25. Roberts, G. O., Rosenthal, J. S.: Optimal scaling for various Metropolis-Hastings algorithms. Stat. Sci. 16, 351-367 (2001).
26. Roberts, G. O., Rosenthal, J. S.: Examples of adaptive MCMC. J. Comput. Graph. Stat. 18(2), 349-367 (2009).
27. Roberts, G. O., Rosenthal, J. S.: Coupling and ergodicity of adaptive MCMC. J. Appl. Probab. 44, 458-475 (2007).
28. Rosenthal, J. S.: Parallel computing and Monte Carlo algorithms. Far East J. Theoret. Stat. 4, 207-236 (2000).
29. Woodard, D. B., Schmidler, S. C., Huber, M.: Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions. Ann. Appl. Probab. 19, 617-640 (2009a).
30. Woodard, D. B., Schmidler, S. C., Huber, M.: Sufficient conditions for torpid mixing of parallel and simulated tempering. Electron. J. Probab. 14, 780-804 (2009b).
31. Zheng, Z.: On swapping and simulated tempering algorithms. Stoch. Process. Their Appl. 104, 131-154 (2003).