56: Computationally Efficient Conjugate Bayesian SAE Models with Benchmarking and Inequality Constraints

Thomas M. Menino Convention & Exhibition Center 

Small-area estimates in official statistics must often be not only accurate but also coherent with known aggregate totals and area-specific logical bounds. Existing methods address benchmarking, inequality constraints, heteroscedastic variance modeling, and spatial dependence, but typically treat these separately rather than within one framework. We develop constrained heteroscedastic area-level models that simultaneously enforce benchmarking and lower-bound constraints, jointly model area-level means and sampling variances, and incorporate spatial dependence. Building on the conjugate framework of Parker et al. (2024), the models retain computational efficiency while allowing richer dependence and coherence than standard approaches. We consider a non-spatial model (CHALM) and a spatial extension (SCHALM) with ICAR structure on the mean and variance. In a simulation study using county-level Iowa corn data, both models substantially improve on direct estimates in RMSE and interval score, with the spatial model best overall. Applied to corn production across eight Midwestern states, both preserve the main geographic pattern while producing smoother, more stable estimates—SCHALM providing the strongest smoothing and the most coherent uncertainty surface.

Small Area Estimation

Benchmarking

Inequality Constraints

Heteroscedastic area-level model

Bayesian Hierarchical Models

Spatial dependence 

Survey Research Methods Section