Dynamic Hierarchical Models

Abstract

An analysis of a time series of cross-sectional data is considered under a Bayesian perspective. Information is modelled in terms of prior distributions and stratified parametric linear models developed by Lindley and Smith and dynamic linear models developed by Harrison and Stevens are merged into a general framework. This is shown to include many models proposed in econometrics and experimental design. Properties of the model are derived and shrinkage estimators reassessed. Evolution, smoothing and passage of data information through the levels of the hierarchy are discussed. Inference with an unknown scalar observation variance is drawn and an extension to the non-linear case is proposed