臺灣博碩士論文加值系統

本篇論文討論 copula models 在生物醫學的應用。Copula model是一種適合描述高維度存活變數的機率模式，在論文中我們討論copula model的兩個重要子家族－mixture model和alpha,beta-family，並提出演算法以電腦模擬方式生成資料。此外透過mixture model具有層級性的特性，我們將其應用在分析家族資料中。針對alpha,beta-family，因為參數alpha,beta和與描述極端情形的相關參數(tail dependence參數) 有直接對應的關係，所以我們考慮在twin study上的應用，此參數可以描述雙胞胎人瑞的關聯性強弱。我們並提出有母數及無母數的方法以估計tail dependence參數。

In the thesis, we discuss applications of copula models in medical research. Copula models are useful for describing multivariate survival data in which the dependence structure of major interest but marginal distributions are less important. We discuss two sub-families of copula models — namely mixture models and the alpha,beta-family. We also propose simulation algorithms to generate data following these models. Since mixture models have a hierarchical structure, we consider their applications in modeling genetic (familial) survival data. Parameters in the alpha,beta-family have a direct relationship with tail dependence parameters. We consider applications in describing the association between lifetimes of twins at very old age. Two estimation procedures are proposed to estimate tail dependence.

第一章 背景簡介 03
1.1 研究動機與背景 03
1.2 論文大綱 05
第二章 Copula Family 文獻回顧與討論 05
2.1 文獻方向 05
2.2 用Mixture概念建構子家族 ( Marshall and Olkin， 1998 ) 09
2.3 Mixture models在家族資料之應用 ( Joe， 1992 ) 11
( 摘錄 (i) 參數: Kendall’ s tau， tail dependence
(ii) extreme cases
(iii) power form 與 AC form 的關係 )
2.4 特殊的 AC 子家族 ( Nelson， 1997 ) 18
2.5 各子家族的關係 19
畫出各 sub-family 的關係
第三章 模擬實驗 20
3.1 生成 mixture models 20
A. 在條件獨立下
B. 在非條件獨立下
3.2 生成 alpha，beta -family 22
A. 方法 ( 利用 rejection method )
B. 實際例子
3.3 模擬結果 26
第四章 雙胞胎研究之回顧與新方向 28
4.1 前言
4.2 描述相關性的參數 29
討論 tau 與其它　measures
4.3 tail dependence參數的應用與估計 32
第五章 結論 36
( 把 family data structure 在其中討論 )
附錄 37

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