Spatio-Temporal Modeling and Spatial Clustering of Curves: A Bayesian Approach Applied to Portuguese Regional Fertility Rates

It is important for social analyses and policy-making to obtain accurate estimates of demographic variables such as age-specific fertility rates, by regions and over time, and the uncertainty associated with such estimation. In this paper, we consider a Bayesian hierarchical model with separable spatio-temporal dependence structure that admits the Markov property and can be estimated by borrowing strength from all regions and years. Further, we explore the local similarity of temporal evolution and dependence by developing a spatial clustering model for temporal or functional data based on Bayesian nonparametric smoothing techniques, such as wavelet shrinkage methods. We extend existing functional mixed-effects model with random block decomposition of the covariance matrix and further, our model allows difference scaling and shrinkage levels of wavelet coefficients across random groups. The traditional empirical Bayes estimators for the hyper-parameters under such random group structure are generally not available, and we derive an empirical procedure to determine a prior distribution to incorporate these parameters in a Gibbs circle. The proposed model is applied to 16-year data.