A Bayesian two-fold small area model for estimation of sub-area means when only area-level aggregate

Thomas M. Menino Convention & Exhibition Center 

Estimating subarea-level means is difficult when only aggregated area-level totals are observed. We propose a two-fold Bayesian framework that uses hierarchical modeling and covariate driven borrowing of strength to recover latent subarea signals. To incorporate known area-level totals, we introduce a Soft Constraint Theorem that modifies the posterior distribution through a Kullback–Leibler divergence projection. This approach enforces the aggregate constraint while retaining the flexibility of the posterior and avoiding the rigidity of hard constraints. We further study the uncertainty of the Bayesian estimators from a frequentist perspective by estimating bias and variance based on corrected Markov chain Monte Carlo samples. Through simulation studies, we show that the proposed method provides a good approximation to the empirical mean squared error

Small area estimation

Hierarchical Bayesian modeling 

Survey Research Methods Section