本論文使用了多維普瓦松分布的EM演算法來插補次世代序列資料的遺失值，並且做了兩類模擬遺失值的資料來檢驗其性能。一類是隨機遺失值的資料，另一類為整行遺失值的資料，並且以孫孝芳教授提供的資料來作為實例。在遺失值為隨機的模擬資料中，使用EM演算法來跟最小鄰近 (K-Nearest Neighbor) 插補法、最小平方法做比較。在整行遺失值的模擬資料中，使用EM演算法來跟轉置最小鄰近插補法、迴歸插補法做比較，並且使用廣義估計方程式來估算真陽率 (true positive rate) 以及偽陽率 (false positive rate)。在實例資料中，使用EM演算法來跟轉置最小鄰近插補法、迴歸插補法做比較，並且使用廣義估計方程式來推測出致病基因。結果顯示EM演算法較其他演算法有效。

This thesis presents an expectation-maximization (EM) algorithm for multivariate Poisson distribution of next-generation sequencing data. We set up two scenarios and conducted simulation studies to examine the performance of multiple imputations with EM algorithm and with other imputation methods. Two kinds of data were simulated—one with randomly removed values as missing values, and the other with the whole column values removed as missing values. Then, we used Professor H. Sunny Sun’s data to analyze the real data. In the data obtained by randomly removing values, the EM algorithm had higher accuracy rates than the weighted adjusted k-nearest neighbor (KNN) method and least squares method did. In the data obtained by removing whole columns, the EM algorithm had higher accuracy rates than the transpose k-nearest neighbor (tKNN) and linear imputation methods did. Also, we used the generalized estimation equation (GEE) to estimate the true positive rates and false positive rates. In the real data, we compared EM algorithm with the tKNN and linear imputation methods, and use GEE to find the diseased genes. The results reveal that compared with other methods, the proposed EM algorithm is more efficient in imputing NGS data for multivariate Poisson distribution.

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