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Start Over Search Limiters Full Text Topic bayes' theorem Publisher academic press inc.
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1. A nonparametric empirical Bayes approach to adaptive minimax estimation.

Author

Jiang, Wenhua and Zhang, Cun-Hui

Subjects
*EMPIRICAL research, *BAYES' theorem, *CHEBYSHEV approximation, *FUNCTIONAL analysis, *NUMERICAL analysis, *GAUSSIAN distribution
Abstract

Abstract: The general maximum likelihood empirical Bayes (GMLEB) method has been proven to possess optimal properties and demonstrated to have superior numerical performance in the Gaussian sequence model. Although it is known that nonparametric function estimation and the Gaussian sequence models are closely related, implementation of the GMLEB in function estimation problems still awaits careful analysis. In this paper, we consider adaptive estimation to inhomogeneous smoothness. We study the extent to which the optimality properties of the GMLEB can be carried out from the Gaussian sequence model to nonparametric function estimation. We demonstrate the proposed method’s superior performance in large sample size settings. [Copyright &y& Elsevier]

Published
2013
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2. Blind source separation with time series variational Bayes expectation maximization algorithm

Author

Sun, Shijun, Peng, Chenglin, Hou, Wensheng, Zheng, Jun, Jiang, Yingtao, and Zheng, Xiaolin

Subjects
*BLIND source separation, *TIME series analysis, *COMPUTER algorithms, *BAYES' theorem, *SIGNAL processing, *GAUSSIAN processes, *MAGNETOENCEPHALOGRAPHY
Abstract

Abstract: This paper presents a variational Bayes expectation maximization algorithm for time series based on Attiasʼ variational Bayesian theory. The proposed algorithm is applied in the blind source separation (BSS) problem to estimate both the source signals and the mixing matrix for the optimal model structure. The distribution of the mixing matrix is assumed to be a matrix Gaussian distribution due to the correlation of its elements and the inverse covariance of the sensor noise is assumed to be Wishart distributed for the correlation between sensor noises. The mixture of Gaussian model is used to approximate the distribution of each independent source. The rules to update the posterior hyperparameters and the posterior of the model structure are obtained. The optimal model structure is selected as the one with largest posterior. The source signals and mixing matrix are estimated by applying LMS and MAP estimators to the posterior distributions of the hidden variables and the model parameters respectively for the optimal structure. The proposed algorithm is tested with synthetic data. The results show that: (1) the logarithm posterior of the model structure increases with the accuracy of the posterior mixing matrix; (2) the accuracies of the prior mixing matrix, the estimated mixing matrix, and the estimated source signals increase with the logarithm posterior of the model structure. This algorithm is applied to Magnetoencephalograph data to localize the source of the equivalent current dipoles. [Copyright &y& Elsevier]

Published
2012
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