Estimation of bayes factors in a class of hierarchical random effects models using a geometrically ergodic MCMC algorithm

Journal of Computational and Graphical Statistics

Volumn 19, Issue 2, 2010, Pages 295-312

  Doss, Hani ^a   Hobert, James P ^a  

^a University of Florida   (United States)

Author keywords

Dirichlet process; Empirical Bayes; Importance sampling; Meta analysis

Indexed keywords

EID: 77956693464     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/jcgs.2010.09182     Document Type: Article

References (26)

1. Antoniak, C. E. (1974), "Mixtures of Dirichlet Processes With Applications to Bayesian Nonparametric Problems," The Annals of Statistics, 2, 1152-1174. [308]
2. Berger, J. O. (1985), Statistical Decision Theory and Bayesian Analysis (2nd ed.), New York: Springer-Verlag. [299]
3. Chan, K. S., and Geyer, C. J. (1994), Comment on "Markov Chains for Exploring Posterior Distributions," by L. Tierney, The Annals of Statistics, 22, 1747-1758. [297,310]
4. Doss, H. (2009), "Hyperparameter and Model Selection for Nonparametric Bayes Problems via Radon-Nikodym Derivatives," technical report, University of Florida, Dept. of Statistics. [308]
5. DuMouchel, W. (1990), "Bayesian Meta-Analysis," in Statistical Methodology in the Pharmaceutical Sciences, New York: Dekker, pp. 509-529. [299]
6. Flegal, J. M., Haran, M., and Jones, G. L. (2008), "Markov Chain Monte Carlo: Can We Trust the Third Significant Figure?" Statistical Science, 23, 250-260. [297,307,310]
7. Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2004), Bayesian Data Analysis (2nd ed.), New York: Chapman & Hall. [296]
8. Geyer, C. J. (1992), "Practical Markov Chain Monte Carlo" (with discussion), Statistical Science, 7, 473-511. [305,310]
9. Harris, R., Beebe-Donk, J., Doss, H., and Burr, D. (2005), "Aspirin, Ibuprofen and Other Non-Steroidal Anti-Inflammatory Drugs in Cancer Prevention: A Critical Review of Non-Selective COX-2 Blockade," Oncology Reports, 13, 559-584. [305,306]
10. Hobert, J. P., and Geyer, C. J. (1998), "Geometric Ergodicity of Gibbs and Block Gibbs Samplers for a Hierarchical Random Effects Model," Journal of Multivariate Analysis, 67, 414-430. [297,298,300,302,310]
11. Ibragimov, I. A., and Linnik, Y. V. (1971), Independent and Stationary Sequences of Random Variables, Gronin-gen: Wolters-Noordhoff. [304]
12. Iwama, T. (2009), "NSAIDs and Colorectal Cancer Prevention," Journal of Gastroenterology, 44 (Supplement 19), 72-76. [305]
13. Jain, S., and Neal, R. M. (2007), "Splitting and Merging Components of a Nonconjugate Dirichlet Process Mixture Model," Bayesian Analysis, 2, 445-472. [309]
14. Jarner, S. F., and Hansen, E. (2000), "Geometric Ergodicity of Metropolis Algorithms," Stochastic Processes and Their Applications, 85, 341-361. [311]
15. Jones, G. L., Haran, M., Caffo, B. S., and Neath, R. (2006), "Fixed-Width Output Analysis for Markov Chain Monte Carlo," Journal ofthe American Statistical Association, 101, 1537-1547. [305,310]
16. Marchev, D., and Hobert, J. P. (2004), "Geometric Ergodicity of van Dyk and Meng's Algorithm for the Multivariate Student's t Model," Journal of the American Statistical Association, 99, 228-238. [311]
17. Mengersen, K. L., and Tweedie, R. L. (1996), "Rates of Convergence of the Hastings and Metropolis Algorithms," The Annals of Statistics, 24, 101-121. [310]
18. Meyn, S. P., and Tweedie, R. L. (1993), Markov Chains and Stochastic Stability, London: Springer-Verlag. [302, 303]
19. Mykland, P., Tierney, L., and Yu, B. (1995), "Regeneration in Markov Chain Samplers," Journal of the American Statistical Association, 90, 233-241. [305]
20. Papaspiliopoulos, O., and Roberts, G. (2008), "Stability of the Gibbs Sampler for Bayesian Hierarchical Models," The Annals of Statistics, 36, 95-117. [311]
21. Roberts, G. O., and Rosenthal, J. S. (1997), "Geometric Ergodicity and Hybrid Markov Chains," Electronic Communications in Probability, 2, 13-25. [310]
22. - (1998), "Markov Chain Monte Carlo: Some Practical Implications of Theoretical Results" (with discussion), The Canadian Journal of Statistics, 26, 5-31. [310]
23. - (1999), "Convergence of Slice Sampler Markov chains," Journal of the Royal Statistical Society, Ser. B, 61, 643-660. [311]
24. Roberts, G. O., and Tweedie, R. L. (1996), "Geometric Convergence and Central Limit Theorems for Multidimensional Hastings and Metropolis Algorithms," Biometrika, 83, 95-110. [310]
25. Roy, V., and Hobert, J. P. (2007), "Convergence Rates and Asymptotic Standard Errors for Markov Chain Monte Carlo Algorithms for Bayesian Probit Regression," Journal of the Royal Statistical Society, Ser. B, 69, 607-623. [310]
26. Smith, T. C, Spiegelhalter, D. J., and Thomas, A. (1995), "Bayesian Approaches to Random-Effects Meta-Analysis: A Comparative Study," Statistics in Medicine, 14, 2685-2699. [296]