Bayesian Estimation of Large Precision Matrix Based on Cholesky Decomposition |
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Authors: | Li Fan Qun Zhang Xin Sheng |
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Institution: | 1.Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233000, P. R. China;2.School of Management, Fudan University, Shanghai 200433, P. R. China |
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Abstract: | In this paper, we consider the estimation of a high dimensional precision matrix of Gaussian graphical model. Based on the re-parameterized likelihood, we obtain the full conditional distribution of all parameters in Cholesky factor. Furthermore, by imposing the prior information, we obtain the shrinkage Bayesian estimator of large precision matrix, and establish the asymptotic distribution of all parameters in the Cholesky factor. At last, we demonstrate our method through the simulation study and an application to telephone call center data. |
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Keywords: | Bayesian estimation Cholesky decomposition graphical model shrinkage |
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