Sparse Bayesian Estimation with High-dimensional Binary Response Data

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吳宣廷(Xuan-Ting Wu) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(Sparse Bayesian Estimation with High-dimensional Binary Response Data)

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摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 貝葉斯
★ 高維度
★ 邏輯式模型
★ 貝式推論
★ 三參數beta 正態

關鍵字(英)

★ Bayesian
★ high-dimensional
★ logistic model
★ Bayesian Inference
★ Three Parameter Beta Normal

論文目次

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

參考文獻

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A.Bhattacharya, A.Chakraborty, Bk.Mallick. (2016). Fast sampling with Gaussian scale mixture priors in high-dimensional regression. Biometrika, 103, 985-991.
A.Bhadr, J.Datta, N.G, Polson B, Willard. (2017). The horseshoe+ estimator of ultra-sparse signals. Bayesian Arial, 12, 1105-1131.
Bai, Ray and Ghosh, Malay. (2018). High-dimensional multivariate posterior consistency under globallocal shrinkage priors. Journal of Multivariate Analysis, 167, 157-170.
Cao, Xuan, Khare, Kshitij and Ghosh, Malay. (2020). High-dimensional posterior consistency for hierarchical non-local priors in regression. Bayesian Anal., 15, 241-262.
Du, Xiaohui, Wang, Xiangzhou, Zhang, Jing and Ni, Guangming. (2021). Leucorrhea microscopy dataset.
Mejia, Amanda, Yue, Yu, Bolin, David, Lindgren, Finn and Lindquist, Martin. (2017). A bayesian general linear modeling approach to cortical surface fmri data analysis. journal of the American Statistical Association.
Penny, William D, Roberts, Stephen J, Curran, Eleanor A and Stokes, Maria J. (2000). Eegbased communication: a pattern recognition approach. IEEE transactions on Rehabil-itation Engineering, 8, 214-215.
Rieger, K., Hong, W., Tusher, V., Tang, J., Tibshirani, R. and Chu, G. (2004). Toxicity from radiation therapy associated with abnormal transcriptional responses to DNA damage. Proceedings of the National Academy of Sciences of the United States of America, 101, 6634-6640.

指導教授

王紹宣(Shao-Hsuan Wang)

審核日期

2022-9-15

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