Examples of adaptive MCMC

Journal of Computational and Graphical Statistics

Volumn 18, Issue 2, 2009, Pages 349-367

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

^a LANCASTER UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

Adaption; Convergence; Hierarchical models; Markov chain monte carlo; Metropolis algorithm; Metropolis within gibbs; Non markovian; Nonconjugate priors

Indexed keywords

EID: 70349290724     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/jcgs.2009.06134     Document Type: Article

References (29)

1. Andrieu, C., and Atchadé, Y. F. (2007), "On the Efficiency of Adaptive MCMC Algorithms," Electronic Communications in Probability, 12, 336-349.
2. Andrieu, C., and Moulines, E. (2003), "On the Ergodicity Properties of Some Adaptive Markov Chain Monte Carlo Algorithms," preprint.
3. Atchadé, Y. F., and Rosenthal, J. S. (2005), "On Adaptive Markov Chain Monte Carlo Algorithms," Bernoulli, 11, 815-828. (Pubitemid 44966970)
4. Bai, Y., Roberts, G. O., and Rosenthal, J. S. (2008), "The Bounded Convergence Condition for Adaptive MCMC," preprint, available at http://probability.ca/jeff/research.html.
5. Bédard, M. (2006a), "Weak Convergence of Metropolis Algorithms for Non-iid Target Distributions," preprint.
6. Bédard, M. (2006b), "Optimal Acceptance Rates for Metropolis Algorithms: Moving Beyond 0.234," preprint.
7. Brockwell, A. E., and Kadane, J. B. (2005), "Identification of Regeneration Times in MCMC Simulation, With Application to Adaptive Schemes," Journal of Computational and Graphical Statistics, 14, 436-458.
8. Efron, B., and Morris, C. (1975), "Data Analysis Using Stein's Estimator and Its Generalizations," Journal of the American Statistical Association, 70 (350), 311-319.
9. 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.
10. Gelman, A., Roberts, G. O., and Gilks, W. R. (1996), "Efficient Metropolis Jumping Rules," in Bayesian Statistics 5, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford, U.K.: Oxford University Press, pp. 599-608.
11. Gilks, W. R., Roberts, G. O., and Sahu, S. K. (1998), "Adaptive Markov Chain Monte Carlo," Journal of the American Statistical Association, 93, 1045-1054.
12. Haario, H., Saksman, E., and Tamminen, J. (1999), "Adaptive Proposal Distribution for Random Walk Metropolis Algorithm," Computational Statistics, 14, 375-395.
13. Haario, H., Saksman, E., and Tamminen, J. (2001), "An Adaptive Metropolis Algorithm," Bernoulli, 7, 223-242. (Pubitemid 33793059)
14. Haario, H., Saksman, E., and Tamminen, J. (2005), "Componentwise Adaptation for High Dimensional MCMC," Computational Statistics, 20, 265-274.
15. Hastings, W. K. (1970), "Monte Carlo Sampling Methods Using Markov Chains and Their Applications," Biometrika, 57, 97-109.
16. Mengersen, K. L., and Tweedie, R. L. (1996), "Rates of Convergence of the Hastings and Metropolis Algorithms," Annals of Statistics, 24, 101-121. (Pubitemid 126090863)
17. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and Teller, E. (1953), "Equations of State Calculations by Fast Computing Machines," Journal of Chemical Physics, 21, 1087-1091.
18. Morris, C. (1983), "Parametric Empirical Bayes Confidence Intervals," in Scientific Inference, Data Analysis, and Robustness, eds. G. E. P. Box, T. Leonard, and C. F. Wu, New York: Academic Press, pp. 25-50.
19. Roberts, G. O., and Rosenthal, J. S. (1998a), "Optimal Scaling of Discrete Approximations to Langevin Diffusions," Journal of the Royal Statistical Society, Ser. B, 60, 255-268.
20. Roberts, G. O., and Rosenthal, J. S (1998b), "Two Convergence Properties of Hybrid Samplers," The Annals of Applied Probability, 8, 397-407. (Pubitemid 128098546)
21. Roberts, G. O., and Rosenthal, J. S (2001), "Optimal Scaling for Various Metropolis-Hastings Algorithms," Statistical Science, 16, 351-367.
22. Roberts, G. O., and Rosenthal, J. S (2005), "Coupling and Ergodicity of Adaptive MCMC," preprint.
23. Roberts, G. O., and Tweedie, R. L. (1996), "Geometric Convergence and Central Limit Theorems for Multidimensional Hastings and Metropolis Algorithms," Biometrika, 83, 95-110.
24. 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. (Pubitemid 127050315)
25. Rosenthal, J. S. (1996), "Analysis of the Gibbs Sampler for a Model Related to James-Stein Estimators," Statistics and Computing, 6, 269-275. (Pubitemid 126724264)
26. Rosenthal, J. S (2004), "Adaptive MCMC Java Applet," available at http://probability.ca/jeff/java/adapt.html.
27. Stewart, A. (2006), personal communication.
28. Tierney, L. (1994), "Markov Chains for Exploring Posterior Distributions" (with discussion), The Annals of Statistics, 22, 1701-1762.
29. Turro, E., Bochkina, N., Hein, A. M. K., and Richardson, S. (2007), "BGX: A Bioconductor Package for the Bayesian Integrated Analysis of Affymetrix GeneChips," BMC Bioinformatics, 8, 439-448. Available at http://www.biomedcentral.com/1471-2105/8/439. (Pubitemid 351187477)