Bayesian Predictive Inference for Multivariate Sample Surveys Balgobin Nandram Abstract: Multivariate observations are available from units in a longitudinal twostage cluster sample design in which the same units or different units can be observed within the same clusters over occasions. The data from all variables are analyzed simultaneously and using the hierarchical Bayesian multivariate normal linear model, an estimator of a general finite population quantity, linear in the population values (e.g., change in finite population mean from one occasion to another), is constructed. Some properties of the point estimator are obtained when the variance components are assumed known. Numerical methods are used when the variance components are unknown. We analyze data on the Patterns of Care Studies, twostage cluster samples of cancer patients each having two scores (bivariate) on two occasions. In particular, we describe the numerical computation of the finite population means (and changes in these means over the two occasions) of the two scores simultaneously. Keywords: Deleted residuals; Gibbs sampler; longitudinal; mean squared error; retransformation; twostage sampling.
