Slice sampling

Annals of Statistics

Volumn 31, Issue 3, 2003, Pages 705-741

  Neal, Radford M ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Adaptive methods; Auxiliary variables; Dynamical methods; Gibbs sampling; Markov chain Monte Carlo; Metropolis algorithm; Overrelaxation

Indexed keywords

EID: 1642370803     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1056562461     Document Type: Review

References (32)

1. ADLER, S. L. (1981). Over-relaxation method for the Monte Carlo evaluation of the partition function for multiquadratic actions. Phys. Rev. D 23 2901-2904.
2. BARONE, P. and FRIGESSI, A. (1990). Improving stochastic relaxation for Gaussian random fields. Probab. Engrg. Inform. Sci. 4 369-389.
3. BESAG, J. and GREEN, P. J. (1993). Spatial statistics and Bayesian computation (with discussion). J. Roy. Statist. Soc. Ser. B 55 25-37, 53-102.
4. CHEN, M.-H. and SCHMEISER, B. W. (1998). Toward black-box sampling: A random-direction interior-point Markov chain approach. J. Comput. Graph. Statist. 7 1-22.
5. DAMIEN, P., WAKEFIELD, J. C. and WALKER, S. G. (1999). Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables. J. R. Stat. Soc. Ser. B Stat. Methodol. 61 331-344.
6. DIACONIS, P., HOLMES, S. and NEAL, R. M. (2000). Analysis of a non-reversible Markov chain sampler. Ann. Appl. Probab. 10 726-752.
7. DOWNS, O. B., MACKAY, D. J. C. and LEE, D. D. (2000). The nonnegative Boltzmann machine. In Advances in Neural Information Processing Systems (S. A. Solla, T. K. Leen and K.-R. Muller, eds.) 428-434. MIT Press, Cambridge, MA.
8. DUANE, S., KENNEDY, A. D., PENDLETON, B. J. and ROWETH, D. (1987). Hybrid Monte Carlo. Phys. Lett. B 195 216-222.
9. EDWARDS, R. G. and SOKAL, A. D. (1988). Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm. Phys. Rev. D 38 2009-2012.
10. FREY, B. J. (1997). Continuous sigmoidal belief networks trained using slice sampling. In Advances in Neural Information Processing Systems (M. C. Mozer, M. I. Jordan and T. Petsche, eds.). MIT Press, Cambridge, MA.
11. GELFAND, A. E. and SMITH, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398-409.
12. GEYER, C. J. and THOMPSON, E. A. (1995). Annealing Markov chain Monte Carlo with applications to ancestral inference. J. Amer. Statist. Assoc. 90 909-920.
13. GILKS, W. R. (1992). Derivative-free adaptive rejection sampling for Gibbs sampling. In Bayesian Statistics (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 641-649. Oxford Univ. Press.
14. GILKS, W. R., BEST, N. G. and TAN, K. K. C. (1995). Adaptive rejection Metropolis sampling within Gibbs sampling. Appl. Statist. 44 455-472.
15. GILKS, W. R., NEAL, R. M., BEST, N. G. and TAN, K. K. C. (1997). Corrigendum: Adaptive rejection Metropolis sampling. Appl. Statist. 46 541-542.
16. GILKS, W. R. and WILD, P. (1992). Adaptive rejection sampling for Gibbs sampling. Appl. Statist. 41 337-348.
17. GREEN, P. J. and HAN, X. (1992). Metropolis methods, Gaussian proposals and antithetic variables. Stochastic Models, Statistical Methods, and Algorithms in Image Analysis (P. Barone et al., eds.). Lecture Notes in Statist. 74 142-164. Springer, New York.
18. GREEN, P. J. and MIRA, A. (2001). Delayed rejection in reversible jump Metropolis-Hastings. Biometrika 88 1035-1053.
19. HASTINGS, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 97-109.
20. HIGDON, D. M. (1996). Auxiliary variable methods for Markov chain Monte Carlo with applications. ISDS discussion paper 96-17, Duke Univ.
21. HOROWITZ, A. M. (1991). A generalized guided Monte Carlo algorithm. Phys. Lett. B 268 247-252.
22. LUNN, D. J., THOMAS, A., BEST, N. and SPIEGELHALTER, D. (2000). WinBUGS - a Bayesian modelling framework: Concepts, structure, and extensibility. Statist. Comput. 10 325-337.
23. METROPOLIS, N., ROSENBLUTH, A. W., ROSENBLUTH, M. N., TELLER, A. H. and TELLER, E. (1953). Equation of state calculations by fast computing machines. J. Chem. Phys. 21 1087-1092.
24. MIRA, A. (1998). Ordering, splicing and splitting Monte Carlo Markov chains. Ph.D. dissertation, School of Statistics, Univ. Minnesota.
25. MIRA, A. and TIERNEY, L. (2002). Efficiency and convergence properties of slice samplers. Scand. J. Statist. 29 1-12.
26. NEAL, R. M. (1994). An improved acceptance procedure for the hybrid Monte Carlo algorithm. J. Comput. Phys. 111 194-203.
27. NEAL, R. M. (1996). Bayesian Learning for Neural Networks. Lecture Notes in Statist. 118. Springer, New York.
28. NEAL, R. M. (1998). Suppressing random walks in Markov chain Monte Carlo using ordered overrelaxation. In Learning in Graphical Models (M. I. Jordan, ed.) 205-228. Kluwer, Dordrecht.
29. NEAL, R. M. (2001). Annealed importance sampling. Statist. Comput. 11 125-139.
30. ROBERTS, G. O. and ROSENTHAL, J. S. (1999). Convergence of slice sampler Markov chains. J. R. Stat. Soc. Ser. B Stat. Methodol. 61 643-660.
31. THOMAS, A., SPIEGELHALTER, D. J. and GILKS, W. R. (1992). BUGS: A program to perform Bayesian inference using Gibbs sampling. In Bayesian Statistics (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 837-842. Oxford Univ. Press.
32. TIERNEY, L. and MIRA, A. (1999). Some adaptive Monte Carlo methods for Bayesian inference. Statistics in Medicine 18 2507-2515.