Bayesian analysis of covariance matrices and dynamic models for longitudinal data

Biometrika

Volumn 89, Issue 3, 2002, Pages 553-566

  Daniels, Michael J ^a   Pourahmadi, Mohsen ^b  

^a E005A Lagomarcino Hall   (United States)

^b NORTHERN ILLINOIS UNIVERSITY   (United States)

Author keywords

Antedependence and autoregressive models; Bayes estimate; Hierarchical model; Markov chain Monte Carlo; Mixed model; Shrinkage estimator; Time series model; Unconstrained parameterisation; Wishart distribution

Indexed keywords

EID: 0038600714     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/89.3.553     Document Type: Review

References (36)

1. ANDERSON, T. W. (1978). Repeated measurements on autoregressive processes. J. Am. Statist. Assoc. 73, 371-8.
2. BARNARD, J., MCCULLOCH, R. & MENG, X. (2000). A natural strategy for modeling covariance matrices with application to shrinkage. Statist. Sinica 10, 1281-311.
3. BROWN, P. J., LE, N. D. & ZIDEK, J. V. (1994). Inference for a covariance matrix. In Aspects of Uncertainty, Ed. P. R. Freeman and A. F. M. Smith, pp. 77-92. Chichester: John Wiley.
4. CHEN, C. F. (1979). Bayesian inference for a normal dispersion matrix and its application to stochastic multiple regression analysis J. R. Statist. Soc. B 41, 235-48.
5. CHIN, T. Y. M., LEONARD, T. & TSUI, K.-W. (1996). The matrix-logarithmic covariance model. J. Am. Statist. Assoc. 91, 198-210.
6. DANIELS, M. J. (1999). A prior for the variance in hierarchical models. Can. J. Statist. 27, 569-80.
7. DANIELS, M. J. & KASS, R. (1999). Nonconjugate Bayesian estimation of covariance matrices and its use in hierarchical models. J. Am. Statist. Assoc. 94, 1254-63.
8. DANIELS, M. J. & KASS, R. (2001). Shrinkage estimators for a covariance matrix. Biometrics 57, 1173-84.
9. DAWID, A. P. (1988). The infinite regress and its conjugate analysis. In Bayesian Statistics 3, Ed. J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, pp. 95-110. Oxford: Clarendon Press.
10. DIGGLE, P. J., LIANG, K. Y. & ZEGER, S. L. (1994). Analysis of Longitudinal Data. Oxford: Oxford University Press.
11. EVERSON, P. & MORRIS, C. (2000). Inference for multivariate normal hierarchical models. J. R. Statist. Soc. B 62, 399-412.
12. GABRIEL, K. R. (1962). Ante-dependence analysis of an ordered set of variables. Ann. Math. Statist. 33, 201-12.
13. GARTHWAITE, P. H. & AL-AWADHI, S. A. (2001). Nonconjugate prior distribution assessment for multivariate normal sampling. J. R. Statist. Soc. B 63, 95-110.
14. GRENANDER, U. & SZEGÖ, G. (1958). Toeplitz Forms and their Applications. Berkeley, CA: University of California Press.
15. JONES, R. H. (1993). Longitudinal Data with Serial Correlation: A State-Space Approach. London: Chapman and Hall.
16. KAILATH, T. (1987). Signal processing applications of some moment problems. In Proc. Symposia in Applied Mathematics. Ed. H. J. Landau, pp. 71-109. Providence, RI: Am. Math. Soc.
17. LAIRD, N. M. & WARE, J. J. (1982). Random-effects models for longitudinal data. Biometrics 38, 973-9.
18. LEONARD, T. & HSU, J. S. (1992). Bayesian inference for a covariance matrix. Ann. Statist. 20, 1669-96.
19. LITTLE, R. J. A. & RUBIN, D. B. (1987). Statistical Analysis with Missing Data. New York: John Wiley & Sons.
20. MACCHIAVELLI, R. E. & ARNOLD, S. F. (1994). Variable order antedependence models. Commun. Statist. A 23, 2683-99.
21. POURAHMADI, M. (1999). Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterisation. Biometrika 86, 677-90.
22. POURAHMADI, M. (2000). Maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix. Biometrika 87, 425-35.
23. POURAHMADI, M. & DANIELS, M. (2002). Dynamic conditionally linear mixed models for longitudinal data. Biometrics, 58, 82-8.
24. RAHIALA, M. (1999). Random coefficient autoregressive models for longitudinal data. Biometrika 86, 718-22.
25. RICHARD, J. F. & STEEL, M. F. J. (1988). Bayesian analysis of systems of seemingly unrelated regression equations under a recursive extended natural conjugate prior density. J. Economet. 38, 7-37.
26. ROVERATO, A. (2000). Cholesky decomposition of a hyper inverse Wishart matrix. Biometrika 87, 99-112.
27. SAS INSTITUTE INC. (1997). SAS/STAT Software: Changes and Enhancements through Release 6.12. Cary, NC: SAS Institute Inc.
28. SEARLE, S., CASELLA, G. & MCCULLOCH, C. (1992). Variance Components. New York: John Wiley.
29. SPIEGELHALTER, D. J., BEST, N. G., GILKS, W. R. & INSKIP, H. (1996). Hepatitis B: A case study in MCMC methods. In Markov Chain Monte Carlo in Practice, Ed. W. R. Gilks, S. Richardson and D. J. Spiegelhalter, pp. 339-58. London: Chapman and Hall.
30. TANABE, K. & SAGAE, M. (1992). An exact Cholesky decomposition and the generalized inverse of the variancecovariance matrix of the multinomial distribution, with applications. J. R. Statist. Soc. B 54, 211-9.
31. TANNER, M. A. & WONG, W. H. (1987). The calculation of posterior distributions by data augmentation. J. Am. Statist. Assoc. 82, 528-40.
32. TSIMIKAS, J. V. & LEDOLTER, J. (1998). Analysis of multi-unit variance components models with state space profiles. Ann. Inst. Statist. Math. 50, 147-64.
33. VERBYLA, A. P. (1993). Modeling variance heterogeneity: Restricted maximum likelihood and diagnostics. J. R. Statist. Soc. B 55, 493-508.
34. WEST, M. & HARRISON, P. J. (1997). Bayesian Forecasting and Dynamic Models, 2nd ed. New York: Springer-Verlag.
35. WEST, M., PRADO, R. & KRYSTAL, A. D. (1999). Evaluation and comparison of EEG traces: Latent structure in nonstationary time series. J. Am. Statist. Assoc. 94, 1083-95.
36. YANG, R. & BERGER, J. O. (1994). Estimation of a covariance matrix using the reference prior. Ann. Statist. 22, 1195-211.