Seemingly unrelated regression is a natural framework for regressing multiple correlated responses on multiple predictors. The model is very flexible, with multiple linear regression and covariance selection models being special cases. However, its practical deployment in genomic data analysis under a Bayesian framework is limited due to both statistical and computational challenges. The statistical challenge is that one needs to infer both the mean vector and the covariance matrix, a problem inherently more complex than separately estimating each. The computational challenge is due to the dimensionality of the parameter space that routinely exceeds the sample size. We propose the use of horseshoe priors on both the mean vector and the inverse covariance matrix. This prior has demonstrated excellent performance when estimating a mean vector or covariance matrix separately. The current work shows these advantages are also present when addressing both simultaneously. A full Bayesian treatment is proposed, with a sampling algorithm that is linear in the number of predictors. MATLAB code implementing the algorithm is freely available from github at this https URL. Extensive performance comparisons are provided with both frequentist and Bayesian alternatives, and both estimation and prediction performances are verified on a genomic data set.
@cite_7 developed the covariate-adjusted precision matrix estimation or CAPME procedure taking a two-stage approach and using a multivariate extension of the Dantzig selector of . Let @math , @math , @math and @math . The estimate of @math in CAPME solves the optimization problem
@cite_7
2312490702
Capon Beamforming Algorithm involves calculating inverse covariance matrix. It's complex to calculate inverse matrix in engineering applications. On the basis of summary of distribution of covariance matrix elements, an improved inverse covariance matrix calculating method is proposed. Simulation shows that the improved algorithm achieves the same accuracy with original algorithm as reducing the computational complexity. (6 pages)