用遺失值的資料配適混合模型(mixtrue models)是一個重要的研究課題。在本文中，在假設隨機遺失訊息?missing at random?（MAR）情況下，我們引進輔助的指標矩陣來處理多變量混合常態模型。我們發展一個新結構的EM演算法可大幅地節省運算時間並且有許多應用，例如：密度估計、分類與遺失值的預測。對於遺失資料的多重設算(multiple impuation)，我們利用吉氏抽樣法(Gibbs sampler)提出一個新的資料擴增（data augmentation）演算法。在考慮不同的人為遺失比例下，我們用一些實例來闡述所提出的方法。 It is an important research issue to deal with mixture models when missing values occur in the data. In this paper, computational strategies using auxiliary indicator matrices are introduced for handling mixtures of multivariate normal distributions in a more efficient manner, assuming that patterns of missingness are arbitrary and missing at random. We develop a novelly structured EM algorithm which can dramatically save computation time and be exploited in many applications, such as density estimation, supervised clustering and prediction of missing values. In the aspect of multiple imputations for missing data, we also offer a data augmentation scheme using the Gibbs sampler. Our proposed methodologies are illustrated through some real data sets with varying proportions of missing values.
