With the rise in popularity of digital Atlases to communicate spatial variation, there is an increasing need for robust small-area estimates. However, current small-area estimation methods suffer from various modeling problems when data are very sparse or when estimates are required for areas with very small populations. These issues are particularly heightened when modeling proportions. Additionally, recent work has shown significant benefits in modeling at both the individual and area levels. We propose a two-stage Bayesian hierarchical small area estimation approach for proportions that can: account for survey design; reduce direct estimate instability; and generate prevalence estimates for small areas with no survey data. Using a simulation study we show that, compared with existing Bayesian small area estimation methods, our approach can provide optimal predictive performance (Bayesian mean relative root mean squared error, mean absolute relative bias and coverage) of proportions under a variety of data conditions, including very sparse and unstable data. To assess the model in practice, we compare modeled estimates of current smoking prevalence for 1,630 small areas in Australia using the 2017-2018 National Health Survey data combined with 2016 census data.

翻译：随着数字地图集在空间变异传播中的普及，对稳健的小区域估计的需求日益增长。然而，当前的小区域估计方法在数据非常稀疏或对人口极少的区域进行估计时，会面临多种建模问题，这些问题在估计比例时尤为突出。此外，最近的研究表明，在个体和区域两个层面进行建模具有显著优势。我们提出了一种用于比例的两阶段贝叶斯分层小区域估计方法，该方法能够：考虑调查设计；降低直接估计的不稳定性；为无调查数据的小区域生成患病率估计。通过模拟研究，我们表明，与现有的贝叶斯小区域估计方法相比，我们的方法能在各种数据条件下（包括极度稀疏和不稳定的数据）提供比例的最优预测性能（贝叶斯均方根相对误差、平均绝对相对偏差和覆盖率）。为了评估该模型的实际应用效果，我们结合2017-2018年国家健康调查数据与2016年人口普查数据，比较了澳大利亚1630个小区域的当前吸烟患病率的估计结果。