We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost-effective method, ranked set sampling enables us to incorporate easily attainable characteristics, as ranking information, into data collection and Bayesian estimation. To handle the special structure of the ranked set samples, we develop a Bayesian estimation approach exploiting the Expectation-Maximization (EM) algorithm in estimating the ranking parameters and Metropolis within Gibbs Sampling to estimate the parameters of the underlying mixture model. Our findings show that the proposed RSS-based Bayesian estimation method outperforms the commonly used Bayesian counterpart using simple random sampling. The developed method is finally applied to estimate the bone disorder status of women aged 50 and older.

翻译：我们考虑在不完美排序集抽样设计下，基于独立顺序统计量对有限混合模型参数进行贝叶斯估计。作为一种经济高效的方法，排序集抽样能够将易于获取的特征（如排序信息）纳入数据收集与贝叶斯估计过程。为处理排序集样本的特殊结构，我们开发了一种贝叶斯估计方法：利用期望最大化算法估计排序参数，并采用吉布斯采样中的Metropolis算法估计基础混合模型参数。研究结果表明，本文提出的基于排序集抽样的贝叶斯估计方法优于采用简单随机抽样的常用贝叶斯方法。最后，我们将所开发方法应用于50岁及以上女性骨骼疾病状态的估计。