Bayesian Predictive Inference for a Finite Population Proportion: Two-Stage Cluster Sampling
针对两阶段整群抽样的二元数据，提出一种贝叶斯预测推断方法，用于估计有限总体比例，并给出先验和后验均值和方差的解析表达式，通过美国国家健康访谈调查数据演示参数选择。
SUMMARY Given binary data from a two-stage cluster sample, we present a method to carry out Bayesian predictive inference for a finite population proportion. Our probabilistic specification should be useful for many surveys of this type and yields simple analytical expressions for the prior and posterior mean and variance. Within cluster k, we assume that the Yki are a random sample from the Bernoulli distribution with probability θk. Conditional on β and τ, θ1,..., θN are a random sample from a beta distribution. Finally, β has a discrete distribution with specified probabilities. We use data from the National Health Interview Survey to illustrate the methodology and to show how to choose values for the parameters in the prior distribution.