<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Fully Bayesian Benchmarking of Small Area Estimation Models

Journal of Official Statistics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"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...

Fully Bayesian Benchmarking of Small Area Estimation Models

Published Online: Mar 17, 2020

Page range: 197 - 223

Received: Nov 01, 2018

Accepted: Sep 01, 2019

DOI: https://doi.org/10.2478/jos-2020-0010

Keywords
Small domain estimation, Bayesian hierarchical model, area-level model, life expectancy

© 2020 Junni L. Zhang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Supplementary Material Details

Fully Bayesian Benchmarking of Small Area Estimation Models

Published Online: Mar 17, 2020

Page range: 197 - 223

Received: Nov 01, 2018

Accepted: Sep 01, 2019

DOI: https://doi.org/10.2478/jos-2020-0010

KeywordsSmall domain estimation, Bayesian hierarchical model, area-level model, life expectancy

© 2020 Junni L. Zhang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Supplementary Material Details

Keywords
Small domain estimation, Bayesian hierarchical model, area-level model, life expectancy