本研究使用排隊理論中的馬可夫模型來建立B型肝炎病毒序列的模型，藉由此理論與模型，使用短時間的行為來預測長時間的行為，如本研究中使用單月突變轉置機率矩陣來預測七個月，一年後以及十八個月後的基因序列(包含核�˙躉P胺基酸)，進而推導出該突變率，並與實際的序列比較後，得到不錯的結果，也間接證明，病毒序列目前的狀態(核�˙�)之轉變，應該傾向與前一個狀態相關，而與更早之前的狀態是獨立的，因此馬可夫模型理論在此領域是十分適用的，能精準預測基因序列就能在演化論上有所助益，而突變率的模型建立，更可以幫助判斷一條序列中哪些片段是具有功能上的重要意義，以及哪些片段是不具有意義的假基因。
此外，在分析與統計資料過程中也發現在B型肝炎病毒基因序列中，某些位置特別容易發生突變，而某些則否;再者，每種核�˙警o生突變的機率近似均勻分配，而胺基酸則否；而不論核�˙藺峸繵羃纂A某些突變組合特別容易發生，有些則否，這些詳細數據在結果分析與討論一章中有詳細描述。

Based on the the Markov Model of the Markov Process theory, we built the transition model of the Hepatitis B Virus Sequence. We may observe the short-term behavior and then predict the long-term conduct by the theory and the model. In this research, we may reason out the Mutation Rate just as using the Matrix of the Mutation Transpose Rate to predict seven months, and we can infer the Mutation Rate from the gene sequences, including the nucleotide and the Amino Acid, after a year as well as eighteen months. Moreover, we will get the good results, and indirectly affirm to the changes for a present phase of the virus sequences, the nucleotide, after being compared with the real sequences. And the changes should tend to relate the last condition with the existent one, while it is independent one earlier on. Therefore, the Markov Process Theory is perfectly suitable for the field. And it is helpful to the evolution that can exactly predict the gene sequences. However, the establishment for the model of the Mutation Rate can help us estimate which section of a sequence has the important meaning on the capabilities, while the other one is an untrue gene which doesn’t have any meaning.
Besides, we may find that some positions are easy to arise the mutation specifically in the Hepatitis B Virus gene sequences, while some others are not. Furthermore, the mutation rate of each nucleotide is similar to the even allocation, but the Amino Acid isn’t as this; and whatever the nucleotide or the Amino Acid, some mutation combination more easily occur, while some don’t. And these particular data will have the strict delineations in the chapter of the analysis for result and discussion.mutation combination more easily occur, while some don’t. And these particular data will have the strict delineations in the chapter of the analysis for result and discussion.

中文摘要 iii
英文摘要 vi
誌 謝 vi
目錄 viii
表次 x
圖次 xii
一. 緒論 1
1.1 研究動機與目的 1
1.2 名詞解釋 1
1.2.1 基因突變 1
1.2.2 基因突變的種類 3
1.2.3 基因突變的後果 4
二. 文獻探討 1
2.1 隨機程序 1
2.2 馬可夫模型的介紹 1
2.3 馬可夫模型的特性與分類 2
2.4 Chapman-Kolmogorov Equation 3
2.5 馬可夫理論的專有名詞解釋 3
2.6 馬可夫理論的相關研究 6
三. 研究方法 7
3.1 研究對象 7
3.2 研究架構與流程 7
3.3 馬可夫模型的應用 8
3.4 資料處理與分析 10
3.4.1 資料前處理 10
3.4.2 計算每個馬可夫模型的轉置機率矩陣 11
3.4.3 預測N個時間間隔後的基因序列 11
3.4.4 驗證預測的正確率 11
3.4.5 預測基因序列之突變率 12
3.4.6 比較真實突變率與預測之突變率 12
四. 系統架構與流程介紹 13
4.1 系統架構與步驟 13
4.1.1 計算單位時間之突變率 15
4.1.2 訓練轉置機率矩陣 15
4.1.3 利用轉置矩陣作預測 15
4.1.4 驗證預測的效果好壞 15
4.2 系統介面與操作 16
4.2.1資料轉換 16
4.2.2 資料分析 16
4.2.3 序列預測 18
4.2.4 突變率預測 20
五. 結果分析與討論 21
5.1 使用四位病患當訓練集之研究結果 21
5.2 使用六位病患當訓練集之研究結果 27
5.2.1 以個別病患來觀察 27
5.2.2 以時間來觀察 32
5.3 以胺基酸為研究對象 35
5.3.1 序列預測正確率 35
5.3.2 突變率預測 37
5.3.3 以時間來觀察 38
5.4 相關問題討論 39
5.4.1 四個病患與六個病患之分析與比較 40
5.4.2 核�˙躉P胺基酸的結果比較 41
六. 結論與未來研究方向 45
6.1 結論與討論 45
6.1.1 核�˙蘇蟔靰瑣鰷v統計 45
6.1.2 胺基酸突變的機率統計 46
6.1.3 以每個位置架構馬可夫模型的正確率 48
6.1.4 突變率預測 48
6.2 未來研究方向 50
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林光賢(民國86)，機率論，華泰書局

王鼎(民國92)，統計學，鼎茂, ISBN:986-7760-91-3