Bayesian analysis of a growth curve model with a general autoregressive covariance structure (Q2711685)

A generalized growth curve model is considered of the form \(Y=X\tau A +\varepsilon\), where \(Y\) is a \(p\times N\) response matrix, \(X\) \((p\times m)\) and \(A\) \((r\times N)\) are known design matrices, and \(\tau\) \((m\times r)\) is unknown. The columns of \(\varepsilon\) are independent \(p\)-variate \(N(0,\Sigma)\), and \(\Sigma=(\sigma_{i,j})\) has the general autoregressive structure, i.e. \(\sigma_{i,j}=\sigma_{|i-j|}\) and \(\sigma_{|i-j|}\) are unknown.NEWLINENEWLINENEWLINEMaximum likelihood estimators and Bayesian posteriors are derived for the unknown parameters of this model. For future observations \(V=X\tau F+\varepsilon^*\) (\(F\) is known, \(\varepsilon^*\) has the same distribution as \(\varepsilon\)) a Bayesian predictive inference technique is developed. The MCMC methodology for forecasting is proposed. Numerical illustrations are presented.