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Bayesian Inference Using Hyper Product Inverse Moment Prior in the Ultrahigh-Dimensional Generalized Linear Models | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 2، شماره 2، اسفند 2022، صفحه 63-90 اصل مقاله (309.01 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2023.15187 | ||
| نویسندگان | ||
| Robabeh Hosseinpour Samim Mamaghani1؛ Farzad Eskandari* 2 | ||
| 1Allameh Tabataba'i University | ||
| 2Allameh, Tabatabai University | ||
| چکیده | ||
| In this paper, we considered a Bayesian hierarchical method using the hyper product inverse moment prior in the ultrahigh-dimensional generalized linear model (UDGLM), that was useful in the Bayesian variable selection. We showed the posterior probabilities of the true model converge to 1 as the sample size increases. For computing the posterior probabilities, we implemented the Laplace approximation. The Simpli ed Shotgun Stochastic Search with Screening (S5) procedure for generalized linear model was suggested for exploring the posterior space. Simulation studies and real data analysis using the Bayesian ultrahigh-dimensional generalized linear model indicate that the proposed method had better performance than the previous models. Keywords: Ultrahigh dimensional; Nonlocal prior; Optimal | ||
| کلیدواژهها | ||
| Ultrahigh dimensional؛ Nonlocal prior؛ Optimal properties؛ Bayesian Variable Selection؛ Generalized Linear Model&lrm | ||
| مراجع | ||
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[1] Xuan Cao, Kshitij Khare, and Malay Ghosh. High-dimensional posterior consistency for hierarchical non-local priors in regression. Bayesian Analysis, 15(1):241{262, 2020. [2] Peter K Dunn, Gordon K Smyth, et al. Generalized linear models with examples in R. Springer, 2018. [3] Jianqing Fan, Yang Feng, Diego Franco Saldana, Richard Samworth, Yichao Wu, and Maintainer Diego Franco Saldana. Package sis. CRAN, https://cran. r-project. org/web/pack-ages/SIS/index. html, 2015. [4] Jianqing Fan and Jinchi Lv. Sure independence screening for ultrahigh dimensional feature space. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(5):849{911, 2008. [5] Jianqing Fan and Rui Song. Sure independence screening in generalized linear models with np-dimensionality. The Annals of Statistics, 38(6):3567{3604, 2010. [6] Todd R Golub, Donna K Slonim, Pablo Tamayo, Christine Huard, Michelle Gaasenbeek, Jill P Mesirov, Hilary Coller, Mignon L Loh, James R Downing, Mark A Caligiuri, et al. Molecular classi cation of cancer: class discovery and class prediction by gene expression monitoring. science, 286(5439):531{537, 1999. [7] Peter D Hoff. A rst course in Bayesian statistical methods, volume 580. Springer, 2009. [8] Rafael A Irizarry, Benjamin M Bolstad, Francois Collin, Leslie M Cope, Bridget Hobbs, and Terence P Speed. Summaries of affymetrix genechip probe level data. Nucleic acids research,31(4):e15{e15, 2003. [9] Wenxin Jiang. On the consistency of bayesian variable selection for high dimensional binary regression and classication. Neural computation, 18(11):2762{2776, 2006. [10] Valen E Johnson and David Rossell. On the use of non-local prior densities in bayesian hypothesis tests. Journal of the Royal Statistical Society: Series B (Statistical Methodology),72(2):143{170, 2010. [11] Valen E Johnson and David Rossell. Bayesian model selection in high-dimensional settings. Journal of the American Statistical Association, 107(498):649{660, 2012. [12] Robert E Kass and Larry Wasserman. A reference bayesian test for nested hypotheses and its relationship to the schwarz criterion. Journal of the american statistical association,90(431):928{934, 1995. [13] Faming Liang, Qifan Song, and Kai Yu. Bayesian subset modeling for high-dimensional generalized linear models. Journal of the American Statistical Association, 108(502):589{606, 2013. [14] Dong C Liu and Jorge Nocedal. On the limited memory bfgs method for large scale optimization. Mathematical programming, 45(1):503{528, 1989. [15] Naveen N Narisetty, Juan Shen, and Xuming He. Skinny gibbs: A consistent and scalable gibbs sampler for model selection. Journal of the American Statistical Association, 2018. [16] Amir Nikooienejad, Wenyi Wang, and Valen E Johnson. Bayesian variable selection for binary outcomes in high-dimensional genomic studies using non-local priors. Bioinformatics,32(9):1338{1345, 2016. [17] Amir Nikooienejad, Wenyi Wang, and Valen E Johnson. Bayesian variable selection for survival data using inverse moment priors. The annals of applied statistics, 14(2):809, 2020. [18] Stephen W Raudenbush, Meng-Li Yang, and Matheos Yosef. Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate laplace approximation. Journal of computational and Graphical Statistics, 9(1):141{157, 2000. [19] Christian P Robert et al. The Bayesian choice: from decision-theoretic foundations to computational implementation, volume 2. Springer, 2007. [20] David Rossell and Donatello Telesca. Nonlocal priors for high-dimensional estimation. Journal of the American Statistical Association, 112(517):254{265, 2017. [21] Guiling Shi, Chae Young Lim, and Tapabrata Maiti. Bayesian model selection for generalized linear models using non-local priors. Computational Statistics & Data Analysis, 133:285{296,2019. [22] Minsuk Shin, Anirban Bhattacharya, and Valen E Johnson. Scalable bayesian variable selection using nonlocal prior densities in ultrahigh-dimensional settings. Statistica Sinica, 28(2):1053, 2018. [23] Luke Tierney and Joseph B Kadane. Accurate approximations for posterior moments and marginal densities. Journal of the american statistical association, 81(393):82{86, 1986. [24] Ho-Hsiang Wu, Marco AR Ferreira, Mohamed Elkhouly, and Tieming Ji. Hyper nonlocal priors for variable selection in generalized linear models. Sankhya A, 82(1):147{185, 2020. | ||
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