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研究生:倪惠芬
研究生(外文):Huey_Fan Ni
論文名稱:使用多變量t分配的穩健性混合模型之貝氏分析
論文名稱(外文):Bayesian Analysis of Robust Mixture modeling Using the Multivariate t Distribution
指導教授:李昭勝李昭勝引用關係
指導教授(外文):Jack C. Lee
學位類別:碩士
校院名稱:國立交通大學
系所名稱:統計所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:39
中文關鍵詞:貝氏分類最大概似估計量馬可夫鏈蒙地卡羅法微弱先驗訊息的事前分配條件預測
外文關鍵詞:Bayesian PredictionGiggs SamplingMaximum likelihood estimationMCMCPosterior modeProper Prior
相關次數:
  • 被引用被引用:1
  • 點閱點閱:433
  • 評分評分:
  • 下載下載:94
  • 收藏至我的研究室書目清單書目收藏:1
有關使用貝氏方法分析混合模型的相關文獻中, 目前尚未發現有對多變量 t 分配的混合模型做深入探討的文章, 我們擬對其做一些較深入的探討。
當資料可以被分成 g 群, 且其中一群或多群的觀察值有較常態分配長的尾端時, 使用多變量 t 分配的混合模型是多變量常態分配的混合模型的穩健性延伸。 由於對混合模型使用貝氏方法做推論並不允許無訊息的事前分配, 所以我們採用對參數提供微弱先驗訊息的事前分配。 在參數估計方面, 我們擬用最大概似估計法與貝氏方法做參數估計及未來個體的預測分析; 關於貝氏計算方法, 採用MCMC做參數估計, 並就MCMC抽樣的結果診斷收斂性。 最後, 以一個實際的例子藉由比較貝氏方法與最大概似估計法對未來個體未觀察到的部分之預測的精確度及對部分觀察到的未來個體之分類的正確性來說明貝氏方法優於最大概似估計法。
Finite mixture models using the multivariate t distribution have been provided as a robust extension of normal mixtures. In this paper, from a Bayesian point of view, we consider estimation of parameters, prediction of future values and classification of partially observed future vectors for the t mixture model. The specification of prior distributions are weakly informative, which may or may not be data-dependent, and proper to avoid causing impossible posterior distributions. For parameter estimation, ECM and ECME algorithms are derived based on the observed data and partially observed future vector. Markov chain Monte Carlo (MCMC) schemes are also developed to obtain more accurate Bayesian inference for parameters. The advantage of the Bayesian approach over the maximum likelihood (ML) method are demonstrated via a real data.
1 Introduction …………………………………………………… 1
2 Finite t mixture model ……………………………………… 3
3 Parameter estimation based on and partially observed
individual ……………………………………………………… 7
4 Bayeian inference using Markov chain Monte Carlo method
……………………………………………………………………… 13
5 Conditional prediction and Bayesian classification … 18
6 Illustration …………………………………………………… 20
7 Concluding remarks …………………………………………… 27
Appendix …………………………………………………………… 28
Reference ………………………………………………………… 37
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