  This article attempts to offer some perspectives on Bayesian inference for
finite population quantities when the units in the population are assumed to
exhibit complex dependencies. Beginning with an overview of Bayesian
hierarchical models, including some that yield design-based Horvitz-Thompson
estimators, the article proceeds to introduce dependence in finite populations
and sets out inferential frameworks for ignorable and nonignorable responses.
Multivariate dependencies using graphical models and spatial processes are
discussed and some salient features of two recent analyses for spatial finite
populations are presented.
