Optimal scaling of Metropolis algorithms: Heading toward general target distributions

Canadian Journal of Statistics

Volumn 36, Issue 4, 2008, Pages 483-503

  Bédard, Mylène ^a   Rosenthal, Jeffrey S ^b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

Acceptance rate; Langevin diffusion; Marginal process; Metropolis algorithm; Scaling; Weak convergence

Indexed keywords

EID: 59149089296     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.1002/cjs.5550360401     Document Type: Article

References (25)

1. M. Bédard (2006). On the Robustness of Optimal Scaling for Random Walk Metropolis Algorithms. Doctoral dissertation, Department of Statistics, University of Toronto.
2. M. Bédard (2007a). Weak convergence of Metropolis algorithms fornon-iid target distributions. The Annals of Applied Probability, 17, 1222-1244.
3. M. Bédard (2007b). Optimal acceptance rates for Metropolis algorithms: Moving beyond 0.234. Stochastic Processes and their Applications, In press: corrected proof available online 31 December 2007.
4. M. Bédard (2008). Efficient sampling using Metropolis algorithms: Applications of optimal scaling results. Journal of Computational and Graphical Statistics, 17, 312-332.
5. M. Bédard, G. Fort & E. Moulines (2008). Optimal scaling for the multiple-try Metropolis algorithm. In preparation.
6. M. Bédard & W. S. Kendall (2008). Weak convergence of RWM algorithms using Dirichlet forms. In preparation.
7. J. Besag & P. J. Green (1993). Spatial statistics and Bayesian computation. Journal of the Royal Statistical Society Series B, 55, 25-38.
8. J. Besag, P. J. Green, D. Higdon & K. Mergensen (1995). Bayesian computation and stochastic systems. Statistical Science, 10, 3-66.
9. L. A. Breyer, M. Piccioni & S. Scarlatti (2002). Optimal scaling of MALA for nonlinear regression. The Annals of Applied Probability, 14, 1479-1505.
10. L. A. Breyer & G. O. Roberts (2000). From Metropolis to diffusions: Gibbs states and optimal scaling. Stochastic Processes and their Applications, 90, 181-206.
11. O. F. Christensen, G. O. Roberts & J. S. Rosenthal (2003). Scaling limits for the transient phase of local Metropolis-Hastings algorithms. Journal of the Royal Statistical Society Series B, 67, 253-269.
12. S. N. Ethier & T. G. Kurtz (1986). Markov Processes: Characterization and Convergence. Wiley, New York.
13. A. Gelman, G. O. Roberts & W. R. Gilks (1996). Efficient Metropolis jumping rules. In Bayesian Statistics V (J. M. Bernardo, J. O. Berger, A. F. David and A. F. M. Smith, eds.), Oxford University Press, pp. 599-608.
14. W. K. Hastings (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
15. J. S. Liu, F. Liang & W. H. Wong (2000). The multiple-try method and local optimization in Metropolis sampling. Journal of the American Statistical Association, 95, 121-134.
16. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller & E. Teller (1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087-1092.
17. A. Mira (2001). On Metropolis-Hastings algorithms with delayed rejection. Metron, 59, 231-241.
18. P. Neal & G. O. Roberts (2006). Optimal scaling for partially updating MCMC algorithms. The Annals of Applied Probability, 16, 475-515.
19. P. Neal, G. O. Roberts & J. Yuen (2007). Optimal scaling of random walk Metropolis algorithms with discontinuous target densities. Technical Report.
20. E. Nummelin (1984). General Irreducible Markov Chains and Non-Negative Operators. Cambridge University Press.
21. C. Pasarica & A. Gelman (2003). Adaptively scaling the Metropolis algorithm using expected squared jumped distance. Technical report, Department of Statistics, Columbia University, New York.
22. G. O. Roberts, A. Gelman & W. R. Gilks (1997). Weak convergence and optimal scaling of random walk Metropolis algorithms. The Annals of Applied Probability, 7, 110-120.
23. G. O. Roberts & J. S. Rosenthal (1998). Optimal scaling of discrete approximations to Langevin diffusions. Journal of the Royal Statistical Society Series B, 60, 255-268.
24. G. O. Roberts & J. S. Rosenthal (2001). Optimal scaling for various Metropolis-Hastings algorithms. Statistical Science, 16, 351-367.
25. C. Sherlock (2006). Methodology for Inference on the Markov Modulated Poisson Process and Theory for Optimal Scaling of the Random Walk Metropolis. Doctoral dissertation, Department of Mathematics and Statistics, Lancaster University.