Markov chain Monte Carlo methods in biostatistics

Statistical Methods in Medical Research

Volumn 5, Issue 4, 1996, Pages 339-355

  Gelman, Andrew ^a   Rubin, Donald B ^b  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; COMPUTER SIMULATION; EPIDEMIOLOGY; HUMAN; MATHEMATICAL COMPUTING; MONTE CARLO METHOD; MULTIVARIATE ANALYSIS; PATHOPHYSIOLOGY; PROBABILITY; REACTION TIME; SCHIZOPHRENIA; STATISTICAL ANALYSIS; STATISTICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; DATA INTERPRETATION, STATISTICAL; HUMANS; LIKELIHOOD FUNCTIONS; MARKOV CHAINS; MATHEMATICAL COMPUTING; MODELS, STATISTICAL; MONTE CARLO METHOD; MULTIVARIATE ANALYSIS; REACTION TIME; SAMPLING STUDIES; SCHIZOPHRENIA;

EID: 0030331026     PISSN: 09622802     EISSN: None     Source Type: Journal    
DOI: 10.1177/096228029600500402     Document Type: Article

References (54)

1. Rubin DB. Using the SIR algorithm to simulate posterior distributions. In: Bernardo J ed. Bayesian statistics 3. Oxford: Oxford University Press, 1988: 395-402.
2. Spiegelhalter D, Thomas A, Best N, Gilks W. BUGS: Bayesian inference using Gibbs sampling, version 0.30. MRC Biostatistics Unit, Cambridge, 1994.
3. Zeger SL, Karim MR. Generalized linear models with random effects: a Gibbs sampling approach. Journal of the American Statistical Association 1991; 86: 79-86.
4. Karim MR, Zeger SL. Generalized linear models with random effects; Salamander mating revisited. Biometrics 1992; 48: 631-44.
5. Dellaportas P, Smith AFM. Bayesian inference for generalized linear and proportional hazards models via Gibbs sampling. Applied Statistics 1993; 42: 443-59.
6. Longford N. Random coefficient models. Oxford: Clarendon Press, 1993.
7. Cowles MK, Carlin BP, Connett JE. Bayesian Tobit modeling of longitudinal ordinal clinical trial compliance data. Research report 93-007, Division of Biostatistics, University of Minnesota, 1993.
8. West M. Modelling with mixtures. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM eds. Bayesian statistics 4. New York: Oxford University Press, 1992: 503-24.
9. Lange N, Carlin BP, Gelfand AE. Hierarchical Bayes models for the progression of HIV infection using longitudinal CD4 T-cell numbers (with discussion). Journal of the American Statistical Association 1992; 87: 615-32.
10. Bacchetti P, Segal MR, Jewell NP. Backcalculation of HIV infection rates (with discussion). Statistical Science 1993; 8: 82-119.
11. Baldi P, Chauvin Y, McClure M, Hunkapiller T. Hidden Markov models of biological primary sequence information. Proceedings of the National Academy of Science USA 1994.
12. Clayton D, Bernardinelli L. Bayesian methods for mapping disease risk. In: Elliott P, Cusick J, English D, Stern R eds. Geographical and environmental epidemiology: methods for small-area studies. Oxford: Oxford University Press, 1992: 205-20.
13. Gilks WR, Richardson S. Analysis of disease risks using ancillary risk factors, with application to job-exposure matrices. Statistics in Medicine 1993; 12: 1703-22.
14. Kuo L, Smith AFM. Bayesian computation for survival models via the Gibbs sampler. In: Klien JP, Goel PK eds. Survival Analysis and Related Topics. New York: Marcel Dekker, 1992.
15. Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian data analysis. New York: Chapman & Hall, 1995.
16. Metropolis N, Rosenbluth AW, Rosenbluth MN et al. Equation of state calculations by fast computing machines. Journal of Chemical Physics 1953; 21: 1087-92.
17. Geman S, Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 1984; 6: 721-41.
18. Tanner MA, Wong WH. The calculation of posterior distributions by data augmentation (with discussion). Journal of the American Statistical Association 1987; 82: 528-50.
19. Gelfand AE, Smith AFM. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 1990; 85: 398-409.
20. Gelfand AE, Hills SE, Racine-Poon A, Smith AFM. Illustration of Bayesian inference in normal data models using Gibbs sampling. Journal of the American Statistical Association 1990; 85: 398-409.
21. Smith AFM, Roberts GO. Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (with discussion). Journal of the Royal Statistical Society B 1993; 55: 3-102.
22. Besag J, Green PJ. Spatial statistics and Bayesian computation (with discussion). Journal of the Royal Statistical Society B 1993; 55: 25-102.
23. Gilks WR, Clayton DG, Spiegelhalter DJ et al. Modelling complexity: applications of Gibbs sampling in medicine (with discussion). Journal of the Royal Statistical Society B 1993; 55: 39-102.
24. Gilks WR, Richardson S, Spiegelhalter D eds. Practical Markov Chain Monte Carlo. New York: Chapman & Hall, 1996.
25. Tanner MA. Tools for statistical inference: methods for the exploration of posterior distributions and likelihood functions, 2nd edn. New York: Springer, 1993.
26. Carlin BP, Louis TA. Bayes and empirical Bayes methods for data analysis. New York: Chapman & Hall, 1996.
27. Gelman A, Rubin DB. Inference from iterative simulation using multiple sequences (with discussion). Statistical Science 1992; 7: 457-511.
28. Gelman A, Roberts G, Gilks W. Efficient Metropolis jumping rules. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM eds. Bayesian statistics 5. New York: Oxford University Press, 1996: 599-608.
29. Dempster AP, Laird NM, Rubin DB. Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society B 1977; 30: 1-38.
30. Meng XL, Rubin DB. Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm. Journal of the American Statistical Association 1991; 86: 899-909.
31. Laird NM, Louis TA. Approximate posterior distributions for incomplete data problems. Journal of the Royal Statistical Society B 1982; 44: 190-200.
32. Breslow NE, Clayton DG. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 1993; 88: 9-25.
33. Hill BM. Inference about variance components in the one-way model. Journal of the American Statistical Association 1965; 60: 806-25.
34. Rubin DB. A noniterative sampling/ importance resampling alternative to the data augmentation algorithm for creating a few imputations when fractions of missing information are modest: the SIR algorithm. Journal of the American Statistical Association 1987; 82: 543-46.
35. Kong A, Liu J, Wong WH. Sequential imputations and Bayesian missing data problems. Journal of the American Statistical Association 1994; 89: 278-88.
36. Hastings WK. Monte-Carlo sampling methods using Markov chains and their applications. Biometrika 1970; 57: 97-109.
37. Tierney L. Markov chains for exploring posterior distributions. Annals of Statistics 1995 (in press).
38. Gelman A. Iterative and non-iterative simulation algorithms. Computing Science and Statistics 1992; 24: 433-38.
39. Gelman A, Rubin DB. A single series from the Gibbs sampler provides a false sense of security. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM eds. Bayesian statistics 4. New York: Oxford University Press, 1996: 625-31.
40. Fosdick LD. Calculation of order parameters in a binary alloy by the Monte Carlo method. Physical Review 1959; 116: 565-73.
41. Liu C, Rubin DB. Markov-normal analysis of iterative simulations before their convergence. Journal of Econometrics 1996; 75: 69-78.
42. Gelman A. Inference and monitoring convergence. In: Gilks W, Richardson S, Spiegelhalter D eds. Practical Markov chain Monte Carlo. New York: Chapman & Hall, 1996: 131-43.
43. Besag J. On the statistical analysis of dirty pictures (with discussion). Journal of the Royal Statistical Society B 1986; 48: 259-302.
44. Cowles MK, Carlin BP. Markov chain Monte Carlo convergence diagnostics: a comparative review. Journal of the American Statistical Association 1996 (in press).
45. Gelman A, Bois FY, Jiang J. Physiological pharmacokinetic analysis using population modeling and informative prior distributions. Journal of the American Statistical Association 1996 (in press).
46. Sinclair AJ, Jerrum MR. Conductance and the rapid mixing property of Markov chains: the approximation of the permanent resolved. Proceedings of the Twentieth Annual Symposium on the Theory of Computing, 1988; 235-44.
47. Applegate D, Kannan A, Polson NG. Random polynomial time algorithms for sampling joint distributions. Technical report 500, Carnegie Mellon University, Department of Statistics, 1990.
48. Gilks WR, Wild P. Adaptive rejection sampling for Gibbs sampling. Applied Statistics 1992; 41: 337-48.
49. Gilks WR, Best NG, Tan KKC. Adaptive rejection sampling for Gibbs sampling. Applied Statistics 1995; 44: 455-72.
50. Hills SE, Smith AFM. Parameterization issues in Bayesian inference (with discussion). In: Bernardo JM, Berger JO, Dawid AP, Smith AFM eds. Bayesian statistics 4. New York: Oxford University Press, 1996: 227-46.
51. Geyer CJ, Thompson EA. Annealing Markov chain Monte Carlo with applications to pedigree analysis. Technical report, School of Statistics, University of Minnesota, 1993.
52. Besag J, Green P, Higdon D, Mengersen K. Bayesian computation and stochastic systems (with discussion). Statistical Science 1995; 10: 3-66.
53. Belin TR, Rubin DB. The analysis of repeated-measures data on schizophrenic reaction times using mixture models Statistics in Medicine 1995; 14: 747-68.
54. Meng XL, Rubin DB. Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 1994; 80: 267-78.