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 混合因子分析(MFA) 方法對於高維度資料之基於模型的密度估計和分群是一個很自然可以聯想到的應用工具, 尤其在樣本數相對於變數的維度來得小時更是如此。然而, 當群集個數不小時, MFA 之因子共變異數矩陣的參數個數會相當的大, 造成估計上的困難。為了進一步減少參數的個數, 混合共同因子分析(MCFA), 其為MFA 的精簡延伸法, 最近已被發展出來分析高維度資料。在本文中, 我們採用貝氏分析方法來配適MCFA, 更明確地說, 貝氏方法將基於感興趣的後驗分佈之隨機抽樣來執行參數估計和後驗推論。對於模型的參數, 採用共軛和弱訊息先驗分佈以確保得到合適的參數後驗分配。我們利用有效的馬可夫鏈蒙地卡羅(Markov Chain Monte Carlo; MCMC) 技術, 其結合了資料擴增法以填補隱藏變數以及吉布斯(Gibbs) 抽樣法來生成參數。進一步地, 為了加速MCMC的收斂速度, 我們亦採用逆貝氏公式(Inverse Bayes formulae; IBF) 結合Gibbs 抽樣法來推論模型。同時, 估計隱藏因子和新個體分類的技術也被探討。模擬研究和實例分析顯示了我們的方法在實際應用上提供令人滿意的結果。
 The mixtures of factor analyzers (MFA) approach is a natural tool for model-baseddensity estimation and clustering of high-dimensional data, especially when the numberof observations is not relatively large than their dimension. However, the numberof parameters in the component-covariance matrices of MFA is quite large whenthe number of clusters is not small. To further reduce the number of parameters,mixtures of common factor analyzers (MCFA) have recently been developed as aparsimonious extension of the MFA to analyze high-dimensional data. In this paper,we adopt a fully Bayesian approach, more specifically a treatment that carriesout estimation and inference based on stochastic sampling of the posterior distributionsof interest, to fitting the MCFA. Natural conjugate and weakly informativepriors on the distributions of model parameters are introduced to ensure properposterior distributions of parameters. We provide an efficient Markov Chain MonteCarlo (MCMC) technique which incorporates data augmentation for imputation oflatent variables with Gibbs sampler for generation of parameters. Futhermore, inorder to accelerate the convergence of MCMC procedure, we also adopt the inverseBayes formulae coupled with Gibbs sampler to infer the MCFA. The techniques forestimation of latent factors and classification of new objects are also investigated.Simulation studies and real-data examples demonstrate that our methodology performssatisfactorily.
 1 簡介11.1 背景. . . . . . . . . . . . . . . 11.2 動機與目的. . . . . . . . . . . . 21.3 概要. . . . . . . . . . . . . . . 32 混合因子分析(MFA).................... 42.1 MFA模型. . . . . . . . . . . . . . 42.2 MFA之先驗與完全條件後驗分佈. . . . . 52.3 MCMC 演算法. . . . . . . . . . . . 82.4 IBF-Gibbs 演算法. . . . . . . . .. 93 混合共同因子分析(MCFA) ...............113.1 MCFA模型. . . . . . . . . . . . . 113.2 MCFA之貝氏模形結構. . . . . . . . . 123.2.1 先驗分佈與超參數設定. . . . . .... 123.2.2 後驗分配推論. . . . . . . . ..... 133.3 演算過程. . . . . . . . . . . . . .153.3.1 MCMC 演算過程. . . . . . . ..... 153.3.2 IBF-Gibbs 抽樣法. . . . . . . .. 164 模擬研究...........................174.1 參數估計表現. . . . . . . . . . . 184.2 配適值精準度. . . . . . . . . . . 224.3 分群表現.........................225 實例分析...........................235.1 義大利酒實際資料分析............... 235.2 模擬研究: 干擾變數的葡萄酒模擬試驗... 296 基因微陣列資料分析...................317 結論..............................39附錄A MFA之完全條件後驗分佈推導.........46附錄B MCFA之完全條件後驗分佈推導........50
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 1 利用貝氏方法預測職業比賽之勝負-以台灣職棒為例 2 以隨機波動模型探討隔夜資訊對股價指數之影響 3 Metropolis-Hasting演算法之研究 4 以吉氏抽樣數值法鑑別影響半導體製造良率的關鍵機台組合 5 一個利用貝氏變數選取方法的超飽和設計分析法 6 信用衍生性商品評價-馬可夫鏈模型

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 1 具遺失反應下多變量t 線性混合模型之貝氏推論 2 貝氏變數選取法於不同種族基因資料的比較 3 結合貝氏網路與激勵理論之推薦機制-電影推薦系統設計 4 多項式馬可夫簡易貝氏分類器結合狄氏先驗分配於基因序列分類之研究 5 混合模型分組資料的貝氏方法 6 計數型資料之貝氏推論 7 聯合方程式架構中參數之貝氏與非貝氏估計法 8 應用倒頻譜分析與貝氏推論於穩態視覺誘發電位為基礎之腦控輸入介面設計之研究 9 變概率貝氏推論之非負矩陣拆解應用於聲音聲源分離 10 結合知識與資料的貝氏網路系統 11 利用貝氏階層年齡、時期、出生世代模型探討台灣肝癌發生率長期趨勢 12 貝氏決策法則用於2x2 MIMO通道容量之改善 13 加速衰變測試下p 分位失效時間之貝氏估計 14 生物對等性之貝氏檢定 15 破壞性物件之加速衰退試驗的貝氏可靠度分析

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