处理狄利克雷模型中的缺失值和删失值
Handling Missingness and Censoring in Dirichlet Models
中文总结 AI 辅助
研究在狄利克雷模型中处理缺失值和删失值的问题，开发EM型算法进行参数估计和基于模型的插补，通过模拟研究和实际数据验证，该方法能更好地保留成分结构，为相关数据提供合适模型。
中文摘要 AI 辅助
基于似然的成分数据推断通常需要完全观测的成分，这阻碍了对单纯形上缺失或删失成分的直接处理。本文在统一的粗化框架下，开发了一种期望最大化（EM）型算法，用于在存在缺失和删失成分的情况下对狄利克雷参数进行最大似然估计。狄利克雷分布为成分数据的典型概率模型，为我们的方法提供了基础。我们的方法在进行参数估计和基于模型的插补时保留了数据的成分结构。通过在包括缺失和删失数据的日益复杂的粗化机制下的模拟研究，评估了估计器和插补的性能，并与现有基于模型的方法和非参数方法进行了比较。最后，用汞形态数据说明了该方法的实际效用，结果表明狄利克雷分布为这些数据提供了合适的模型，且我们的方法比其他方法能更好地保留观测到的成分结构。
英文摘要
Likelihood-based inference for compositional data generally requires fully observed compositions, hindering the direct treatment of missing or censored components on the simplex. In this paper, we develop an expectation-maximisation (EM)-type algorithm for maximum likelihood estimation of the Dirichlet parameters in the presence of missing and censored components under a unified coarsening framework. The Dirichlet distribution---the canonical probability model for compositional data, which plays a role analogous to that of the multivariate normal distribution for unconstrained multivariate data---provides the foundation for our methodology. Our methodology preserves the compositional structure of the data while simultaneously performing parameter estimation and model-based imputation. We evaluate the performance of our estimators and imputations through a simulation study under increasingly complex coarsening mechanisms, including both missing and censored data. We compare our method with an existing model-based approach and a nonparametric alternative. Finally, we illustrate the practical utility of our methodology using mercury speciation data, in which compositions are only partially observed because of detection limits and incomplete speciation. Our results indicate that the Dirichlet distribution provides a suitable model for these data and that our method yields imputations that better preserve the observed compositional structure than competing approaches.
