Optimal scaling of discrete approximations to Langevin diffusions

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

Volumn 60, Issue 1, 1998, Pages 255-268

  Roberts, Gareth O ^a   Rosenthal, Jeffrey S ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

Hastings Metropolis algorithm; Langevin algorithm; Markov chain Monte Carlo method; Weak convergence

Indexed keywords

EID: 0000936678     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00123     Document Type: Article

References (17)

1. Besag, J. and Green, P. J. (1993) Spatial statistics and Bayesian computation (with discussion). J. R. Statist. Soc. B, 55, 25-37, 53-102.
2. Durrett, R. (1991) Probability: Theory and Examples. Pacific Grove: Wadsworth and Brooks.
3. Ethier, S. N. and Kurtz, T. G. (1986) Markov processes, characterization and convergence. New York: Wiley.
4. Gelman, A., Roberts, G. O. and Gilks, W. R. (1994) Efficient Metropolis jumping rules. Research Report 94-10. Statistical Laboratory, University of Cambridge, Cambridge.
5. Grenander, U. and Miller, M. I. (1994) Representations of knowledge in complex systems (with discussion). J. R. Statist. Soc. B, 56, 549-603.
6. Hastings, W. K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
7. Kennedy, A. D. and Pendleton, B. (1991) Acceptances and autocorrelations in hybrid Monte Carlo. Nucl. Phys. B, suppl., 20, 118-121.
8. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A. and Teller, E. (1953) Equations of state calculations by fast computing machines. J. Chem. Phys., 21, 1087-1091.
9. Mountain, R. D. and Thirumalai, D. (1994) Quantitative measure of efficiency of Monte Carlo simulations. Physica A, 210, 453-460.
10. Neal, R. M. (1993) Probabilistic inference using Markov chain Monte Carlo methods. Technical Report CRG-TR-93-1. Department of Computer Science, University of Toronto, Toronto.
11. _ (1994) An improved acceptance procedure for the hybrid Monte Carlo algorithm. J. Computnl Phys., 111, 194-203.
12. Phillips, D. B. and Smith, A. F. M. (1994) Bayesian model comparison via jump diffusions. Technical Report 94-20. Imperial College of Science, Technology and Medicine, London.
13. Roberts, G. O., Gelman, A. and Gilks, W. R. (1997) Weak convergence and optimal scaling of random walk Metropolis algorithms. Ann. Appl. Probab., 7, 110-120.
14. Roberts, G. O. and Tweedie, R. L. (1996) Exponential convergence of Langevin diffusions and their discrete approximations. Bernoulli, 2, 341-363.
15. Rossky, P. J., Doll, J. D. and Friedman, H. L. (1978) Brownian dynamics as smart Monte Carlo simulation. J. Chem. Phys., 69, 4628-4633.
16. Smith, A. F. M. and Roberts, G. O. (1993) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (with discussion). J. R. Statist. Soc. B, 55, 3-23, 53-102.
17. Wolfram, S. (1988) Mathematica: a System for Doing Mathematics by Computer. New York: Addison-Wesley.