On the value of derivative evaluations and random walk suppression in Markov Chain Monte Carlo algorithms

Statistics and Computing

Volumn 14, Issue 1, 2004, Pages 23-38

  Gustafson, Paul ^a   Macnab, Ying C ^a,b   Wen, Sijin ^c  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b Ctr Hlth Care Innov/Improvement   (Canada)

^c UNIVERSITY OF TEXAS MD ANDERSON CANCER CENTER   (United States)

Author keywords

Hybrid Monte Carlo; Langevin Monte Carlo; Markov chain Monte Carlo; Metropolis Hastings algorithm; Random walk suppression

Indexed keywords

EID: 3843130660     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:STCO.0000009413.87656.ef     Document Type: Article

References (27)

1. Besag J., York J., and Mollié A. 1991. Bayesian image restoration, with two applications in spatial statistics (with discussion). Annals of the Institute of Statistical Mathematics 43 1-20.
2. Christensen O.F., Moller J., and Waagepetersen R. 2001. Geometric ergodicity of Metropolis-Hastings algorithms for conditional simulation in generalised linear mixed models. Methodology and Computing in Applied Probability 3: 309-327.
3. Duane S., Kennedy A.D., Pendleton B.J., and Roweth D. 1987. Hybrid Monte Carlo. Physics Letters B 195: 216-222.
4. Gamerman D. 1997. Sampling from the posterior distribution in generalized linear mixed models. Statistics and Computing 7: 57-68.
5. Gelfand A.E. and Smith A.F.M. 1990. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85: 398-409.
6. Gelman A., Roberts G.O., and Gilks W. 1996. Efficient Metropolis jumping rules. In: Berger J.O., Bernardo J.M., Dawid A.P., and Smith A.F.M.) Bayesian Statistics 5. Oxford University Press, pp. 599-607.
7. Gelman A. and Rubin D.B. 1992. Inference from iterative simulation using multiple sequences. Statistical Science 7: 457-472.
8. Gustafson P. 1997. Large hierarchical Bayesian analysis of multivariate survival data. Biometrics 53: 230-242.
9. Gustafson P. 1998a. A guided walk Metropolis algorithm. Statistics and Computing 8: 357-364.
10. Gustafson P. 1998b. Flexible Bayesian modelling for survival data. Lifetime Data Analysis 4: 281-299.
11. Hastings W.K. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57: 97-109.
12. Horowitz A.M. 1991. A generalized guided Monte Carlo algorithm. Physics Letters B 268: 247-252.
13. Ishwaran H. 1999. Applications of hybrid Monte Carlo to Bayesian generalized linear models: Quasicomplete separation and neural networks. Journal of Computational and Graphical Statistics 8: 779-799.
14. Leroux B.G., Lei X., and Breslow N. 1999. Estimation of disease rates in small areas: A new mixed model for spatial dependence. In: Halloran M.E. and Berry D.A., (Eds.), Statistical Models in Epidemiology, the Environment and Clinical Trials. New York: Springer, pp. 179-192.
15. Leroux B.G. 2000. Modelling spatial disease rates using maximum likelihood. Statistics in Medicine 19: 2321-2332.
16. MacNab Y.C. 2003a. Hierarchical Bayesian spatial modelling of small-area rates of non-rare disease. Statistics in Medicine 22: 1761-1773.
17. MacNab Y.C. 2003b. Hierarchical Bayesian modelling of spatially correlated health service outcome and utilization rates. Biometrics 59: 305-316.
18. MacNab Y.C. and Dean C.B. 2000. Parametric bootstrap and penalized quasi-likelihood inference in conditional autoregressive models. Statistics in Medicine 19: 2421-2435.
19. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., and Teller E. 1953. Equations of state calculations by fast computing machines. Journal of Chemical Physics 21: 1087-1092.
20. Neal R.M. 1993. Bayesian learning via stochastic dynamics. In: Giles C.L., Hanson S.J., and Cowan J.D. (Eds.), Advances in Neural Information Processing Systems 5. San Mateo, California, Morgan Kaufmann, pp. 475-482.
21. Neal R.M. 1996. Bayesian learning for neural networks. Lecture Notes in Statistics No. 118, New York, Springer-Verlag.
22. Neal R.M. 1998. Suppressing random walks in Markov chain Monte Carlo using ordered overrelaxation. In: Jordan M.I. (Ed.), Learning in Graphical Models. Dordrecht, Kluwer Academic Publishers, pp. 205-225.
23. Roberts G.O., Gelman A., and Gilks W.R. 1997. Weak convergence and optimal scaling of random walk Metropolis algorithms. Annals of Applied Probability 7: 110-120.
24. Roberts G.O. and Rosenthal J.S. 1998. Optimal scaling of discrete approximations to Langevin diffusions. Journal of the Royal Statistical Society B 60: 255-268.
25. Roberts G.O. and Rosenthal J.S. 2001. Optimal scaling for various Metropolis-Hastings algorithms. Statistical Science 16: 351-367.
26. Roberts G.O. and Tweedie R.L. 1996. Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli 2: 341-363.
27. Rue H. 2001. Fast sampling of Gaussian Markov random fields with applications. Journal of the Royal Statistical Society B 63: 325-338.