Title: 使用多變量 t 分配的穩健性混合模型之貝氏分析Bayesian Analysis of Robust Mixture modeling Using the Multivariate t Distribution Authors: 倪惠芬Huey_Fan Ni李昭勝Jack C. Lee統計學研究所 Keywords: 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;Bayesian Prediction;Giggs Sampling;Maximum likelihood estimation;MCMC;Posterior mode;Proper Prior Issue Date: 2001 Abstract: 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. URI: http://140.113.39.130/cdrfb3/record/nctu/#NT900337009http://hdl.handle.net/11536/68389 Appears in Collections: Thesis