Bayesian linear models with unknown design over finite alphabets

Abstract

Our topic is the reconstruction of the unknown matrices S and{omega} for the multivariate linear model Y = S{omega} +{varepsilon} under the assumption that the entries of S are drawn from the finite alphabet [A] = 0, 1 and{omega} is a weight matrix. While a frequentist method has recently been proposed for this purpose, a Bayesian approach seems also desirable. We therefore provide a new hierarchical Bayesian method for this inferential task. Our approach provides estimates of the posterior that may be used to quantify uncertainty. Since matching permutations in both S and{omega} lead to the same reconstruction S{omega}, we introduce an order-preserving shrinkage prior to establish identifiability with respect to permutations.