Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA.
Department of Statistics, Allameh Tabataba'i University, Tehran, Iran.
Stat Med. 2024 Aug 30;43(19):3723-3741. doi: 10.1002/sim.10144. Epub 2024 Jun 18.
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.
我们考虑从不完全有序集抽样设计产生的独立顺序统计量中对有限混合模型的参数进行贝叶斯估计。作为一种具有成本效益的方法，有序集抽样使我们能够轻松地将易于获得的特征（如排序信息）纳入数据收集和贝叶斯估计中。为了处理有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（EM）算法来估计排序参数，以及 Metropolis 在内的 Gibbs 抽样来估计基础混合模型的参数。我们的研究结果表明，所提出的基于 RSS 的贝叶斯估计方法优于常用的基于简单随机抽样的贝叶斯方法。最后，该方法应用于估计 50 岁及以上女性的骨骼疾病状况。
