Shrinkage Bayes Estimation for Matrix-Variate Normal Mean Matrix ‏‎under‎ Balanced Loss Function, By Hamid Karamikabir

Research

Title	Shrinkage Bayes Estimation for Matrix-Variate Normal Mean Matrix ‏‎under‎ Balanced Loss Function
Type	Presentation
Keywords	Balanced loss function, Bayes estimator,‏ Image ‎denoising, ‎Matrix-variate normal ‎distribution,‎ Shrinkage estimation.
Researchers	Hamid Karamikabir (First researcher)

Abstract

We study Bayesian estimation of the mean matrix in a matrix-variate normal distribution with known covariances and a conjugate prior. Under a balanced matrix composite loss function, we derive the Bayes estimator as a convex combination of the posterior mean and the observed data, controlled by a shrinkage parameter $\omega \in [0,1]$. The posterior mean formula $\Theta_n = \frac{1}{2}(\Theta_0 + X)$ is established. A simulation study using non-diagonal AR(1) covariances confirms the theoretical findings, showing that the optimal $\omega$ lies strictly between zero and one under high noise, with the optimal estimator achieving $38.4\%$ MSE reduction over the posterior mean. Performance is evaluated using MSE, PSNR, and SSIM metrics.