On the infinite swapping limit for parallel tempering

Multiscale Modeling and Simulation

Volumn 10, Issue 3, 2012, Pages 986-1022

  Dupuis, Paul ^a   Liu, Yufei ^a   Plattner, Nuria ^a   Doll, J D ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Empirical measure; Gibbs measures; Large deviations; Monte Carlo; Parallel tempering; Rate of convergence; Relative entropy

Indexed keywords

EMPIRICAL MEASURE; GIBBS MEASURE; LARGE DEVIATIONS; MONTE CARLO; PARALLEL TEMPERING; RATE OF CONVERGENCE; RELATIVE ENTROPY;

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; IMPORTANCE SAMPLING; MEASUREMENTS; OPTIMIZATION;

TEMPERING;

EID: 84866989174     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/110853145     Document Type: Article

References (25)

1. L. Breiman, Probability Theory, Addison-Wesley, Reading, MA, 1968.
2. M. D. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, I., Comm. Pure Appl. Math., 28 (1975), pp. 1-47.
3. P. Dupuis and R. S. Ellis, A Weak Convergence Approach to the Theory of Large Deviations, John Wiley & Sons, New York, 1997.
4. D. J. Earl and M. W. Deem, Parallel tempering: Theory, applications, and new perspectives, Phys. Chem. Chem. Phys., 7 (2005), pp. 3910-3916.
5. S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York, 1986.
6. C. J. Geyer, Markov chain Monte Carlo maximum likelihood, in Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, New York, 1991, American Statistical Association, Alexandria, VA, pp. 156-163.
7. C. Kipnis and S. R. S. Varadhan, Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions, Comm. Math. Phys., 104 (1986), pp. 1-19.
8. D. A. Kofke, On the acceptance probability of replica-exchange Monte Carlo trials, J. Chem. Phys., 117 (2002), pp. 6911-6914.
9. H. J. Kushner, Approximation and Weak Convergence Methods for Random Processes with Applications to Stochastic System Theory, MIT Press, Cambridge, MA, 1984.
10. J. S. Liu, Monte Carlo Strategies in Scientific Computing, Springer-Verlag, New York, 2004.
11. S. P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability, Springer-Verlag, London, 1993.
12. P. H. Peskun, Optimum Monte Carlo sampling using Markov chains, Biometrika, 60 (1973), pp. 607-612.
13. R. Pinsky, On evaluating the Donsker-Varadhan I-function, Ann. Probab., 13 (1985), pp. 342-362.
14. N. Plattner, J. D. Doll, P. Dupuis, H. Wang, Y. Liu, and J. E. Gubernatis, An infinite swapping approach to the rare-event sampling problem, J. Chem. Phys., 135 (2011), 134111.
15. C. Predescu, M. Predescu, and C. V. Ciobanu, On the efficiency of exchange in parallel tempering Monte Carlo simulations, J. Phys. Chem. B, 109 (2005), pp. 4189-4196.
16. C. Presescu, M. Presescu, and C. V. Ciobanu, The incomplete beta function law for parallel tempering sampling of classical canonical systems, J. Phys. Chem., 120 (2004), pp. 4119-4128.
17. J. Rosenthal, Asymptotic variance and convergence rates of nearly periodic MCMC algorithms, J. Amer. Statist. Assoc., 98 (2003), pp. 169-177.
18. P. J. Rossky, J. D. Doll, and H. L. Friedman, Brownian dynamics as smart Monte Carlo, J. Chem. Phys., 69 (1978), pp. 4628-4633.
19. D. Sindhikara, D. J. Emerson, and A. E. Roitberg, Exchange often and properly in replica exchange molecular dynamics, J. Chem. Theory Comput., 6 (2010), pp. 2804-2808.
20. D. Sindhikara, Y. Meng, and A. E. Roitberg, Exchange frequency in replica exchange molecular dynamics, J. Chem. Phys., 128 (2008), 024103.
21. Y. Sugita and Y. Okamoto, The incomplete beta function law for parallel tempering sampling of classical canonical systems, Chem. Phys. Lett., 314 (1999), pp. 141-151.
22. R. H. Swendsen and J. S. Wang, Replica Monte Carlo simulation of spin glasses, Phys. Rev. Lett., 57 (1986), pp. 2607-2609.
23. L. Tierney, A note on Metropolis-Hastings kernels for general state space, Ann. Appl. Probab., 8 (1998), pp. 1-9.
24. D. Wales, Energy Landscapes: Applications to Clusters, Biomolecules and Glasses, Cambridge University Press, Cambridge, UK, 2003.
25. D. B. Woodard, S. C. Schmidler, and M. Huber, Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions, Ann. Appl. Probab., 19 (2009), pp. 617-640.