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.

中文翻译：

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小区域估计模型的完全贝叶斯基准

摘要由社会，人口和地理变量定义的小区域的估计对于官方统计越来越重要。为了克服样本量小的问题，统计学家通常会得出基于模型的估计值。但是，如果进行汇总，则基于模型的估计值通常与通过更直接的方法获得的汇总估计值（基准）不一致。对于小面积估算的用户，估算之间缺乏一致性可能会带来问题。标杆管理方法已广泛用于执行协议。从基准化之后产生完整的后验分布的意义上讲，完全贝叶斯基准化方法可以为所有感兴趣的量提供不确定性的连贯度量，但是对完全贝叶斯基准化方法的研究是有限的。我们提供了一种灵活的完全贝叶斯基准测试方法，该方法可用于多种模型和基准测试。我们通过将可能性乘以衡量与基准一致的概率分布来修正可能性。我们概述了马尔可夫链蒙特卡罗方法，从基准后验分布中生成样本。我们提供两个模拟，以及一个对英语和威尔士人的预期寿命的应用。