Fully Bayesian Benchmarking of Small Area Estimation Models

Estimates for small areas defined by social, demographic, and geographic variables are increasingly important for official statistics. To overcome problems of small sample sizes, statisticians usually derive model-based estimates. When aggregated, however, the model- based estimates typically do not agree with aggregate estimates (benchmarks) obtained through more direct methods. This lack of agreement between estimates can be problematic for users of small area estimates. Benchmarking methods have been widely used to enforce agreement. Fully Bayesian benchmarking methods, in the sense of yielding full posterior distributions after benchmarking, can provide coherent measures of uncertainty for all quantities of interest, but research on fully Bayesian benchmarking methods is limited. We present a flexible fully Bayesian approach to benchmarking that allows for a wide range of models and benchmarks. We revise the likelihood by multiplying it by a probability distribution that measures agreement with the benchmarks. We outline Markov chain Monte Carlo methods to generate samples from benchmarked posterior distributions. We present two simulations, and an application to English and Welsh life expectancies.