Ascent-based Monte Carlo expectation-maximization

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 67, Issue 2, 2005, Pages 235-251

  Caffo, Brian S ^a   Jank, Wolfgang ^b   Jones, Galin L ^c  

^a JOHNS HOPKINS UNIVERSITY   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

EM algorithm; Empirical Bayes estimates; Generalized linear mixed models; Importance sampling; Markov chain; Monte Carlo methods

Indexed keywords

EID: 16244422648     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2005.00499.x     Document Type: Article

References (32)

1. Billingsley, P. (1995) Probability and Measure, 3rd edn. New York: Wiley.
2. Booth, J. G. and Hobert, J. P. (1999) Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. J. R. Statist. Soc. B, 61, 265-285.
3. Booth, J. G., Hobert, J. P. and Jank, W. S. (2001) A survey of Monte Carlo algorithms for maximizing the likelihood of a two-stage hierarchical model. Statist. Modllng, 1, 333-349.
4. Caffo, B. S., Booth, J. G. and Davison, A. C. (2002) Empirical sup rejection sampling. Biometrika, 89, 745-754
5. Christensen, O. F. and Ribeiro, Jr, P. J. (2002) geoRglm - a package for generalised linear spatial models. R News, 2, 26-28.
6. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977) Maximum likelihood from incomplete data via the EM algorithm. J. R. Statist. Soc. B, 39, 1-22.
7. Diggle, P. J., Tawn, J. A. and Moyeed, R. A. (1998) Model-based geostatistics. Appl. Statist., 47, 299-326.
8. Geyer, C. J. (1994) On the convergence of Monte Carlo maximum likelihood calculations. J. R. Statist. Soc. B, 56, 261-274.
9. Gueorguieva, R. and Agresti, A. (2001) A correlated probit model for joint modeling of clustered binary and continuous responses. J. Am. Statist. Ass., 96, 1102-1112.
10. Hobert, J. P. and Geyer, C. J. (1998) Geometric ergodicity of Gibbs and block Gibbs samplers for a hierarchical random effects model. J. Multiv. Anal., 67, 414-430.
11. Hobert, J. P., Jones, G. L., Presnell, B. and Rosenthal, J. S. (2002) On the applicability of regenerative simulation in Markov chain Monte Carlo. Biometrika, 89, 731-743.
12. Ihaka, R. and Gentleman R. (1996) R: a language for data analysis and graphics. J. Comput. Graph. Statist., 5, 299-314.
13. Jank, W. and Booth J. G. (2003) Efficiency of Monte Carlo EM and simulated maximum likelihood in two-stage hierarchical models. J. Comput. Graph. Statist., 12, 214-229.
14. Jones, G. L., Haran, M. and Caffp, B. S. (2004) Output analysis for Markov chain Monte Carlo simulations. Technical Report. School of Statistics, University of Minnesota, Minneapolis.
15. Jones, G. L. and Hobert, J. P. (2001) Honest exploration of intractable probability distributions via Markov chain Monte Carlo. Statist. Sci., 16, 312-334.
16. Kendall, M. G. and Stuart, A. (1958) The Advanced Theory of Statistics, vol. 1. London: Griffin.
17. Lange, K. (1999) Numerical Analysis for Statisticians. New York: Springer.
18. Levine, R. A. and Casella, G. (2001) Implementations of the Monte Carlo EM algorithm. J. Comput. Graph. Statist., 10, 422-439.
19. Littell, R. C., Milliken, G. A., Stroup, W. W. and Wolfinger, R. D. (1996) SAS System for Mixed Models. Gary: SAS Institute.
20. Louis, T. A. (1982) Finding the observed information matrix when using the EM algorithm. J. R. Statist. Soc. B, 44, 226-233.
21. McCulloch, C. E. (1994) Maximum likelihood variance components estimation for binary data. J. Am. Statist. Ass., 89, 330-335.
22. McCulloch, C. E. (1997) Maximum likelihood algorithms for generalized linear mixed models. J. Am. Statist. Ass., 92, 162-170.
23. Meyn, S. P. and Tweedie, R. L. (1993) Markov Chains and Stochastic Stability. London: Springer.
24. Mykland, P., Tierney, L. and Yu, B. (1995) Regeneration in Markov chain samplers. J. Am. Statist. Ass., 90, 233-241.
25. Nummelin, E. (1984) General Irreducible Markov Chains and Non-negative Operators. London: Cambridge University Press.
26. Polyak, B. T. and Juditsky, A. B. (1992) Acceleration of stochastic-approximation by averaging. SIAM J. Control Optimzn, 30, 838-855.
27. Quintana, F. A., Liu, J. S. and del Pino, G. E. (1999) Monte Carlo EM with importance reweighting and its applications in random effects models. Comput. Statist. Data Anal., 29, 429-444.
28. Robert, C. P. and Casella, G. (1999) Monte Carlo Statistical Methods. New York: Springer.
29. Searle, S. R., Casella, G. and McCulloch, C. E. (1992) Variance Components. New York: Wiley.
30. Shi, J. Q. and Copas, J. (2002) Publication bias and meta-analysis for 2 × 2 tables: an average Markov chain Monte Carlo EM algorithm. J. R. Statist. Soc. B, 64, 221-236.
31. Wei, G. C. G. and Tanner, M. A. (1990) A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms. J. Am. Statist. Ass., 85, 699-704.
32. Wu, C. F. J. (1983) On the convergence properties of the EM algorithm. Ann. Statist., 11, 95-103.