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Biometrika 2002 89(3):553-566; doi:10.1093/biomet/89.3.553
© 2002 by Biometrika Trust
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Bayesian analysis of covariance matrices and dynamic models for longitudinal data

Michael J.Daniels1 and Mohsen Pourahmadi2

1 Department of Statistics, Iowa State University, Ames, Iowa 50011, U.S.Amdaniels{at}iastate.edu 2 Division of Statistics, Northern Illinois University, DeKalb, Illinois 60115, U.S.A.pourahm{at}math.niu.edu

Parsimonious modelling of the within-subject covariance structure while heeding its positive-definiteness is of great importance in the analysis of longitudinal data.Using the Cholesky decomposition and the ensuing unconstrained and statistically meaningful reparameterisation, we provide a convenient and intuitive framework for developing conditionally conjugate prior distributions for covariance matrices and show their connections with generalised inverse Wishart priors. Our priors offer many advantages with regard to elicitation, positive definiteness, computations using Gibbs sampling, shrinking covariances toward a particular structure with considerable flexibility, and modelling covariances using covariates. Bayesian estimation methods are developed and the results are compared using two simulation studies. These simulations suggest simpler and more suitable priors for the covariance structure of longitudinal data.

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

Received January 2001. Revised December 2001


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