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| 研究生： |
范靜宜 Fan, Gin-Yi |
|---|---|
| 論文名稱： |
分析失去部分訊息的貝氏更新計算方法 Bayesian updating methods for the analysis of censored data. |
| 指導教授： | 姜志銘 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2006 |
| 畢業學年度： | 95 |
| 語文別： | 中文 |
| 論文頁數： | 62 |
| 中文關鍵詞： | 貝氏 、準貝氏法 、平均變異數和 、吉氏取樣器 |
| 外文關鍵詞： | Bayes, quasi-Bayes, Average variance sum, Gibbs sampler |
| 相關次數： | 點閱：191 下載：110 |
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對於使用貝氏法來處理部份區分(partially-classified)或是失去部分訊息資料的類別抽樣(categorical sampling with censored data)，大多建立在「誠實回答」(truthful reporting)以及「無價值性失去部分訊息」(non-informative censoring)的前提下。Jiang(1995)及Jiang and Dickey(2006)取消以上兩個限制，提出貝氏解並利用準貝氏法(quasi-Bayes)來求近似解，而Jiang and Ko(2004)也利用吉氏取樣器(Gibbs sampler)來近似這類問題的貝氏解。本文首先嘗試利用Kuroda, Geng and Niki(2001)所提的“平均變異數和(average variance sum)”估計法
來應用到我們問題的貝氏解。在小樣本時，數值上我們可求得貝氏解，因此本文另一個重點為在小樣本時比較以上三種方法估計值的準確性，並考慮先驗參數(prior)的選取對估計的影響。
本文更進一步證明若選取到某種特殊的先驗參數時，利用“平均變異數和”的方法所計算出來的結果會和
準貝氏法的估計結果相同，而且皆等於用貝氏法計算出的結果。
摘要................................................1
1簡介...............................................2
2.多元伯努利抽樣.....................................3
3.準貝氏法(quasi-Bayes)在不完整多元伯努利上應用的介紹...7
4.平均變異數和(average variance sum)的介紹
4.1平均變異數和在不完整多元伯努利上的應用..............10
4.2平均變異數和的性質...............................14
5.吉氏取樣器(Gibbs sampler)的介紹
5.1吉氏取樣器.......................................18
5.2簡單的收斂說明...................................19
5.3吉氏取樣器在不完整多元伯努利上的應用................21
6.準貝氏法、平均變異數和與吉氏取樣器的模擬結果...........24
6.1小樣本數(1<n<9)的模擬結果.........................25
6.2中樣本數(10<n<15)的模擬結果.......................29
7.結論..............................................32
參考書目.............................................34
附錄 A 數據整理.......................................36
最大相對誤差折線圖與平均相對誤差折線圖.............43
B Fortran 95 程式...............................49
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[2] Dickey, J. M., Jiang, T. J., and Kadane, J. B. (1987). "Bayesian Methods for Censored Categorical Data," Journal of the American Statistical Association, 82, 773-781.
[3] Gelfand, A. E., and Smith, A. F. M. (1990). "Sampling-Based Approaches to Calculating Marginal Densities," Journal of the American Statistical Association, 85, 398-409.
[4] Hastings, W. K. (1970). "Monte Carlo Sampling Methods Using Markov Chains and their Application,"Biometrika, 57, 97-109.
[5] Jiang, T. J. (1995), "Quasi-Bayes Sequential Method for Categorical Data Under Informative Censoring,"Technical Report, 1995-02, Dept. of Mathematical Sciences, National Chengchi University.
[6] Jiang, T. J., and Dickey, J. M. (2006), "Quasi-Bayes Methods for Categorical Data Under Informative Censoring," to be published.
[7] Jiang, T. J., Kadane, J. B., and Dickey, J. M. (1992), "Computation of Carlson's Multiple Hypergeometric Function for Bayesian Applications," Journal of Computational and Graphical Satatistics, 1, 231-251.
[8] Jiang, T. J., and Ko, Li-Wen (2004), "The Gibbs Sampler for Bayesian Analysis on Censored Categorical Data," 2004 Proceeding of the Section on Bayesian Statistical Science of the American Statistical Assocition, 97-103.
[9] Karson, M. J., and Wrobleski, W. J. (1970), "A Bayesian Analysis of Binomial Data with a Partially Informative Category," in Proceedings of the Bussiness and Economic Statistics Section, American Statistical Association, 523-534.
[10] Kuroda, M., Geng, Z., and Niki, N. (2001) "Bayesian Sequential Learning from Incomplete Data on Decomposable Graphical Models," Journal of the Japanese Society of Computational Statistics, 14, 11-29.
[11] Geman, S., and Geman, D. (1984), "Stochastic Relation, Gibbs Distribution and the Bayesian Restortion of Image," IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
[12] 汪為開(1995), "失去部份訊息而有價值的類別資料依循序程序處理之計算方法,"碩士論文-國立政治大學應用數學系研究所.
[13] 柯力文(2003), "準貝氏法與吉氏取樣器在處理失去部分訊息資料上的比較,"碩士論文-國立政治大學應用數學系研究所.
[14] 羅文宜(2005), "具有訊息的遺失資料計算方法之比較,"碩士論文-國立政治大學應用數學系研究所.