Bayesian analysis of growth curves with AR(1) dependence (Q1378813)

The generalized growth curve model with AR(1) dependence is defined as \(Y=X\tau A+\varepsilon\), where \(\tau\) is an unknown vector and \(X\) and \(A\) are known design matrices. The random error vector \(\varepsilon\) is normal with zero mean vector and covariance matrix \(\Sigma=\sigma^2C\), where the matrix \(C\) has the form \((\rho^{| i-j|})\). \(\sigma^2\), \(\sigma^2>0\), and \(\rho\), \(|\rho|<1\), are unknown parameters. The authors consider Bayesian analysis of this model. Both parameter estimation and prediction of future values are discussed. Results are illustrated with real and simulated data.