本文的第一部分目的是研究 Binding Potential (BP) image 和憂鬱症之間的關係，利用 BP image (或再加入其他的變數，如：憤怒性行為)來分類病人是否患有憂鬱症。我們提出兩個綜合的方法，步驟一是將 BP image 經由小波轉換（去除雜訊），步驟二是利用 Regularized Optimal Affine Discriminant (方法一)以及 Support Vector Machine (方法二)利用步驟一得到的小波係數(以及其他的影響因子)進行分類。我們比較這兩種擁有 L1 限制式方法的判錯率，敏感度，和特異度，同時將和分類有關的小波係數轉回原大腦影像，藉以了解大腦哪些區域與分類憂鬱症較有關係。
在第二部分，我們將提出新的非線性及非常態混合效應模型，此模型的應用可以相當廣
泛，我們將其用來配適卵巢癌病人的 CA125 當做範例，並且資料是隨時間變化的。這個模型可配合使用許多偏斜分佈來配適資料，而偏斜 t 分佈是我們選擇的其中一個分佈，其相關性質也會在本文的後段做介紹。

The aim of the first part of this study is to use binding potential (BP) image (and/or
other covariates,such as aggression) to differentiate major mental disorders (MMD) patients from normal controls. We propose two methods to classify these two groups. First, we transform the BP image to the wavelet domain to reduce noise; Second, apply Regularized Optimal Affine Discriminant (method 1) and support vector machine (method 2) to the obtained wavelet coefficients to classify the two groups. We compare the misclassification rates, sensitivities, and specificities for these two methods with L1 penalty. In addition, we transform back the wavelet coefficients important to classification to the original image domain; these coefficient images would help us to understand with which brain regions the MMD is associated.
In the second part, we bring up a new nonlinear and non-normal mixed-effects model,
applications of this model can be quite extensive. we use this model to fit CA125 of ovarian cancer which are changing with time as an example. This model can be used to fit data in conjunction with many skewed distributions, and skew t distribution is just a distribution which we have chosen. Its related properties will be presented at the last half of this thesis.

論文審定書 i
誌謝 ii
摘要 iii
Abstract iv
1 研究動機與目的 1
2 資料描述 4
2.1 憂鬱症介紹 4
2.2 資料介紹 5
3 方法介紹 6
3.1 Wavelet Transform 6
3.2 Fivefold 9
3.3 Regularized Optimal Affine Discriminant(ROAD) 10
3.4 Support Vector Machine with L1 Penalty(SVM) 12
3.5 Random Forest 14
3.6 AdaBoost 14
4 第一部分實際資料分析結果15
4.1 ROAD 與SVM 比較結果 15
4.2 Random Forest 與AdaBoost 比較結果 16
4.3 將原始資料增加影響因子(Aggression) 18
5 憂鬱症對應實際大腦影像區塊 19
6 分佈介紹 21
6.1 多維偏斜常態分佈(Multivariate Skew Normal Distribution) 21
6.2 多維偏斜t 分佈(Multivariate Skew t Distribution) 22
7 模型介紹 23
7.1 General Model . 23
7.2 Likelihood 26
7.2.1 隨機效應項服從多維常態分佈 26
7.2.2 隨機效應項服從多維偏斜 t 分佈 26
8 結語與討論 28
8.1 結語 28
8.2 討論 28
參考文獻 29
附錄 30

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