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題名 具有訊息的遺失資料計算方法之比較
作者 羅文宜
貢獻者 姜志銘
羅文宜
關鍵詞 遺失資料
貝氏方法
準貝氏法
吉氏取樣器
日期 2004
上傳時間 17-Sep-2009 13:50:26 (UTC+8)
摘要 對於處理部份區分或是失去部分訊息資料的類別抽樣的問題，在許多領域裡皆有許多的應用。貝氏方法雖可處理這類問題，但是貝氏方法對這類問題的計算相當耗時，因此對於這種問題的後驗估計，Jiang (1995) 及 Jiang and Dickey (2005) 提出quasi-Bayes方法，Jiang and Ko (2004)利用Gibbs sampler來近似(approximate)這些後驗估計值。但是這兩種近似方法的優劣，因為貝氏方法計算上的困難，一直沒有任何文章作這方面的比較，本文突破計算上的某些限制，在小樣本時，對這兩種近似方法的近似度(相對於真正的貝氏值)作比較，進一步探討使用兩種比較方法的優劣。
參考文獻 Casella. G., and George, E. I. (1992), "Explaining the Gibbs sampler," The American Statistician, 46, 167-174.
Dickey, J.M., Jiang, T. J., and Kadane, J. B. (1987), "Bayes Methods for Censored Categorical Data," Journal of the American Statistical Association, 85, 398-409.
Gelfand, A. E., Smith, A. F. M. (1990), "Sampling-Based Approaches to Calculating Marginal Densities," Journal of the American Statistical Association, 85, 398-409.
Hastings, W. K. (1970), "Monte Carlo Sampling Methods Using Markov Chains and their Application," Biometrika, 57, 97-109.
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.
Jiang, T. J., and Dickey, J. M. (2005), "Quasi-Bayes Methods for Categorical Data Under Informative Censoring," to be published.
Jiang, T. J., Kadane, J. B., and Dickey, J. M. (1992), "Computation of Carlson`s Multiple Hypergeometric Function R for Bayesian Applications," Journal of Computational and Graphical Statistics, 1, 231-251.
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 Association, 97-103.
Karson, M. J., and Wrobleski, W. J. (1970), "A Bayesian Analysis of Binomial Data With a Partially Informative Category," in Proceedings of the Business and Economic Statistics Section, American Statistical Association, 532-534.
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.
汪為開(1995), "失去部分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.
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.
描述 碩士
國立政治大學
應用數學研究所
92751006
93
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0927510061
資料類型 thesis
dc.contributor.advisor 姜志銘zh_TW
dc.contributor.author (Authors) 羅文宜zh_TW
dc.creator (作者) 羅文宜zh_TW
dc.date (日期) 2004en_US
dc.date.accessioned 17-Sep-2009 13:50:26 (UTC+8)-
dc.date.available 17-Sep-2009 13:50:26 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 13:50:26 (UTC+8)-
dc.identifier (Other Identifiers) G0927510061en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/32608-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 92751006zh_TW
dc.description (描述) 93zh_TW
dc.description.abstract (摘要) 對於處理部份區分或是失去部分訊息資料的類別抽樣的問題，在許多領域裡皆有許多的應用。貝氏方法雖可處理這類問題，但是貝氏方法對這類問題的計算相當耗時，因此對於這種問題的後驗估計，Jiang (1995) 及 Jiang and Dickey (2005) 提出quasi-Bayes方法，Jiang and Ko (2004)利用Gibbs sampler來近似(approximate)這些後驗估計值。但是這兩種近似方法的優劣，因為貝氏方法計算上的困難，一直沒有任何文章作這方面的比較，本文突破計算上的某些限制，在小樣本時，對這兩種近似方法的近似度(相對於真正的貝氏值)作比較，進一步探討使用兩種比較方法的優劣。zh_TW
dc.description.tableofcontents 1 簡介........................................................3
2 計算方法的介紹..............................................4
2.0 貝氏法在不完整多元伯努利上的應用.........................4
2.1 準貝氏法在不完整多元伯努利上的應用.......................8
2.2 吉氏取樣器..............................................11
2.2.1 吉氏取樣器的介紹.....................................11
2.2.2 簡單的收斂說明.......................................13
2.2.3 吉氏取樣器在不完整多元伯努利上的應用.................15
3 Fortran程式................................................18
3.1 迴圈單一化..............................................18
3.2 溢位....................................................21
4 準貝氏法與吉氏取樣器的比較結果.............................27
5 結論.......................................................41
A 兩種比較方法之平均相對誤差的折線圖.........................44
B 兩種比較方法在觀察值order不同時估計值的MSE折線圖...........48
C Fortran 90程式.............................................50		zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0927510061en_US
dc.subject (關鍵詞) 遺失資料zh_TW
dc.subject (關鍵詞) 貝氏方法zh_TW
dc.subject (關鍵詞) 準貝氏法zh_TW
dc.subject (關鍵詞) 吉氏取樣器zh_TW
dc.title (題名) 具有訊息的遺失資料計算方法之比較zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Casella. G., and George, E. I. (1992), "Explaining the Gibbs sampler," The American Statistician, 46, 167-174.zh_TW
dc.relation.reference (參考文獻) Dickey, J.M., Jiang, T. J., and Kadane, J. B. (1987), "Bayes Methods for Censored Categorical Data," Journal of the American Statistical Association, 85, 398-409.zh_TW
dc.relation.reference (參考文獻) Gelfand, A. E., Smith, A. F. M. (1990), "Sampling-Based Approaches to Calculating Marginal Densities," Journal of the American Statistical Association, 85, 398-409.zh_TW
dc.relation.reference (參考文獻) Hastings, W. K. (1970), "Monte Carlo Sampling Methods Using Markov Chains and their Application," Biometrika, 57, 97-109.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) Jiang, T. J., and Dickey, J. M. (2005), "Quasi-Bayes Methods for Categorical Data Under Informative Censoring," to be published.zh_TW
dc.relation.reference (參考文獻) Jiang, T. J., Kadane, J. B., and Dickey, J. M. (1992), "Computation of Carlson`s Multiple Hypergeometric Function R for Bayesian Applications," Journal of Computational and Graphical Statistics, 1, 231-251.zh_TW
dc.relation.reference (參考文獻) 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 Association, 97-103.zh_TW
dc.relation.reference (參考文獻) Karson, M. J., and Wrobleski, W. J. (1970), "A Bayesian Analysis of Binomial Data With a Partially Informative Category," in Proceedings of the Business and Economic Statistics Section, American Statistical Association, 532-534.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) 汪為開(1995), "失去部分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.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW