ﻻ يوجد ملخص باللغة العربية
We develop singular value shrinkage priors for the mean matrix parameters in the matrix-variate normal model with known covariance matrices. Our priors are superharmonic and put more weight on matrices with smaller singular values. They are a natural generalization of the Stein prior. Bayes estimators and Bayesian predictive densities based on our priors are minimax and dominate those based on the uniform prior in finite samples. In particular, our priors work well when the true value of the parameter has low rank.
Shrinkage prior are becoming more and more popular in Bayesian modeling for high dimensional sparse problems due to its computational efficiency. Recent works show that a polynomially decaying prior leads to satisfactory posterior asymptotics under r
This study proposes a novel hierarchical prior for inferring possibly low-rank matrices measured with noise. We consider three-component matrix factorization, as in singular value decomposition, and its fully Bayesian inference. The proposed prior is
We investigate the frequentist coverage properties of Bayesian credible sets in a general, adaptive, nonparametric framework. It is well known that the construction of adaptive and honest confidence sets is not possible in general. To overcome this p
For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as Kibble-type, no
Consider the problem of simultaneous testing for the means of independent normal observations. In this paper, we study some asymptotic optimality properties of certain multiple testing rules induced by a general class of one-group shrinkage priors in