🤖 AI Summary
Bayesian inference for finite-population surveys is challenging when sampling units exhibit complex dependencies (e.g., spatial, network, or structural) and nonresponse is nonignorable.
Method: We propose a unified hierarchical modeling framework that integrates graphical models and spatial random fields to characterize multivariate dependence; formally adopts the “unapologetic Bayesian” paradigm, embedding design-based weights (e.g., Horvitz–Thompson) naturally into prior and likelihood specifications; incorporates causal ignorability analysis to ensure identifiability under missing-not-at-random (MNAR) mechanisms; and employs MCMC and variational inference for scalable computation.
Contribution/Results: The framework achieves improved small-area estimation accuracy and more reliable uncertainty quantification in two empirical spatial finite-population analyses. It rigorously reconciles design-based consistency with model-based flexibility, providing theoretical guarantees for valid Bayesian inference under complex survey designs and nonignorable nonresponse.
📝 Abstract
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.