In population studies, it is standard to sample data via designs in which the population is divided into strata, with the different strata assigned different probabilities of inclusion. Although there have been some proposals for including sample survey weights into Bayesian analyses, existing methods require complex models or ignore the stratified design underlying the survey weights. We propose a simple approach based on modeling the distribution of the selected sample as a mixture, with the mixture weights appropriately adjusted, while accounting for uncertainty in the adjustment. We focus for simplicity on Dirichlet process mixtures but the proposed approach can be applied more broadly. We sketch a simple Markov chain Monte Carlo algorithm for computation, and assess the approach via simulations and an application.

中文翻译：

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使用样本调查权重的非参数贝叶斯建模

在人口研究中，标准的做法是通过设计对数据进行抽样，其中将人口分为不同的阶层，不同的阶层分配不同的包含概率。尽管有人建议将样本调查权重纳入贝叶斯分析，但现有方法需要复杂的模型或忽略调查权重背后的分层设计。我们提出了一种简单的方法，基于将所选样本的分布建模为混合物，适当调整混合物权重，同时考虑调整中的不确定性。为了简单起见，我们重点关注狄利克雷过程混合物，但所提出的方法可以更广泛地应用。我们绘制了一个简单的马尔可夫链蒙特卡罗算法进行计算，并通过模拟和应用评估该方法。