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研究生: 吳宣廷
Xuan-Ting Wu
論文名稱: Sparse Bayesian Estimation with High-dimensional Binary Response Data
指導教授: 王紹宣
Shao-Hsuan Wang
口試委員:
學位類別: 碩士
Master
系所名稱: 理學院 - 統計研究所
Graduate Institute of Statistics
論文出版年: 2022
畢業學年度: 110
語文別: 英文
論文頁數: 32
中文關鍵詞: 貝葉斯高維度邏輯式模型貝式推論三參數beta 正態
外文關鍵詞: Bayesian, high-dimensional, logistic model, Bayesian Inference, Three Parameter Beta Normal
相關次數: 點閱:4下載:0
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  • 我們在具有高維矩陣值協變量數據的邏輯線性模型中考慮貝葉斯估計,特別是在超高維數據中。這項研究的動機是在經典的邏輯式模型中擴展貝葉斯方法。所提出的估計可以應用於在分類方法上,比較多的案例是有關於有無疾病,事件的是否發生,例如張量判別分析以及常見的成像研究、遺傳學等。我們用模擬研究和陶瓷樣品的化學成分數據集來展示所提出的方法。


    We consider Bayesian estimation in a logistic linear model with high-dimensional matrixvalued covariate data, especially in ultra-high-dimensional data. The motivation for this
    study is to develop the Bayesian approach in classical logistic-style models. The proposed estimates can be applied to classification problems, most of which are related to the presence or absence of diseases and the occurrence of events, such as tensor discriminant analysis and common imaging studies, genetics, etc. Simulation studies and a dataset of the chemical composition of a dataset demonstrate the proposed method.

    1 Introduction 1 1.1 MCMC method and Gibbs sampling Algorithm 2 1.2 P´olya-Gamma (PG) distribution 6 2 Logistic regression model 11 3 Bayesian method for logistic model 13 3.1 Three Parameter Beta Normal family (TPBN) 13 3.2 Bayesian method 15 3.3 Algorithm 15 4 Numerical Study 17 4.1 Simulation 17 4.2 Empirical Study 20 5 Conclusion 22 Bibliography 23

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