Bayesian modeling of several covariance matrices and some results on propriety of the posterior for linear regression with correlated and/or heterogeneous errors

Journal of Multivariate Analysis

Volumn 97, Issue 5, 2006, Pages 1185-1207

  Daniels, Michael J ^a  

^a University of Florida ^*  (United States)

Author keywords

Bayes Factor; Cholesky decomposition; Improper priors; Markov chain Monte Carlo; Spectral decomposition; Variance correlation decomposition

Indexed keywords

EID: 33645892912     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2005.06.001     Document Type: Article

References (33)

1. Albert J.H., and Chib S. Bayesian analysis of binary and polychotomous response data. J. Amer. Statist. Assoc. 88 (1993) 669-679
2. Banfield J.D., and Raftery A.E. Model-based Gaussian and non-Gaussian clustering. Biometrics 49 (1993) 803-821
3. Barnard J., McCulloch R., and Meng X.-L. Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage. Statist. Sinica 10 4 (2000) 1281-1311
4. Boik R.J. Spectral models for covariance matrices. Biometrika 89 1 (2002) 159-182
5. Bollerslev T. Modeling the coherence in short run nominal exchange rates: a multivariate generalized arch model. Rev. Econom. Statist. 72 (1990) 498-505
6. Chib S. Marginal likelihood from the Gibbs output. J. Amer. Statist. Assoc. 90 (1995) 1313-1321
7. Daniels M.J. A prior for the variance in hierarchical models. Canad. J. Statist. 27 (1999) 567-578
8. Daniels M.J. Shrinkage priors for the dependence structure in longitudinal data. J. Statist. Plann. Inference 127 (2005) 119-130
9. Daniels M.J., and Hogan J.W. Reparameterizing the pattern-mixture model for sensitivity analyses under informative drop-out. Biometrics 56 (2000) 1241-1248
10. Daniels M.J., and Kass R.E. Nonconjugate Bayesian estimation of covariance matrices and its use in hierarchical models. J. Amer. Statist. Assoc. 94 (1999) 1254-1263
11. Daniels M.J., and Kass R.E. Shrinkage estimators for covariance matrices. Biometrics 57 4 (2001) 1173-1184
12. Daniels M.J., and Pourahmadi M. Bayesian analysis of covariance matrices and dynamic models for longitudinal data. Biometrika 89 3 (2002) 553-566
13. Dickey J.M. The weighted likelihood ratio linear hypotheses on normal location parameters. Ann. Math. Statist. 42 (1971) 204-223
14. Flury B.N. Common principal components in k groups. J. Amer. Statist. Assoc. 79 (1984) 892-898
15. Flury B.N. Asymptotic theory for common principal component analysis. Ann. Statist. 14 (1986) 418-430
16. Flury B.N. Common Principal Components and Related Multivariate Models (1988), Wiley, New York
17. Gelfand A.E., and Ghosh S.K. Model choice: a minimum posterior predictive loss approach. Biometrika 85 (1998) 1-11
18. Hawkins D.M. Comment on A review and analysis of the Mahalanobis-Taguchi system (Pkg: p1-30). Technometrics 45 1 (2003) 25-29
19. Hogan J.W., and Laird N.M. Model-based approaches to analysing incomplete longitudinal and failure time data. Statist. Med. 16 (1997) 259-272
20. Lin X., Raz J., and Harlow S.D. Linear mixed models with heterogeneous within-cluster variances. Biometrics 53 (1997) 910-923
21. Manly B.F.J., and Rayner J.C.W. The comparison of sample covariance matrices using likelihood ratio tests. Biometrika 74 (1987) 841-847
22. Marshall A.W., and Olkin I. Inequalities-Theory of Majorization and its Applications (1979), Academic Press, New York
23. Pinheiro J.C., and Bates D.M. Unconstrained parametrizations for variance-covariance matrices. Statist. Comput. 6 (1996) 289-296
24. Pourahmadi M. Joint mean-covariance models with applications to longitudinal data: unconstrained parameterisation. Biometrika 86 (1999) 677-690
25. Pourahmadi M., and Daniels M.J. Dynamic conditionally linear mixed models for longitudinal data. Biometrics 58 1 (2002) 225-231
26. M. Pourahmadi, M.J. Daniels, T. Park, Simultaneous modelling of the cholesky decomposition of several covariance matrices, 2005, submitted for publication.
27. Silverman B.W. Density Estimation for Statistics and Data Analysis (1999), Chapman & Hall Ltd, London
28. Smith A.F.M., and Roberts G.O. Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (Disc: p53-102). J. Roy. Statist. Soc. Ser. B, Methodol. 55 (1993) 3-23
29. Spiegelhalter D.J., Best N.G., Carlin B.P., and van der Linde A. Bayesian measures of model complexity and fit (Pkg: p583-639). J. Roy. Statist. Soc. Ser. B, Methodol. 64 4 (2002) 583-616
30. D. Sun, S. Ni, Bayesian analysis of vector-autoregressive models with noninformative priors. J. Statist. Plann. Inference 121 (2) (2004) 291-309.
31. Verbyla A.P. Modelling variance heterogeneity: Residual maximum likelihood and diagnostics. J. Roy. Statist. Soc. Ser. B, Methodol. 55 (1993) 493-508
32. Verdinelli I., and Wasserman L. Computing Bayes factors using a generalization of the Savage-Dickey density ratio. J. Amer. Statist. Assoc. 90 (1995) 614-618
33. Yang R., and Berger J.O. Estimation of a covariance matrix using the reference prior. Annals Statist. 22 (1994) 1195-1211