Jointly Distributed Mean and Mixing Coefficients for Bayesian Source Separation using MCMC and ICM

Abstract

Recent source separation work has described a model which assumes a nonzero overall mean and incorporates prior knowledge regarding it. This is significant because source separation models that have previously been presented, have assumed that the overall mean is zero. However, this work specified that the prior distribution which quantifies available prior knowledge regarding the overall mean be independent of the mixing coefficient matrix. The current paper, generalizes this work by quantifying available prior information regarding the overall mean and mixing matrix with the use of joint prior distributions. This prior knowledge in the prior distri- butions is incorporated into the inferences along with the current data. Conjugate normal, and generalized conjugate normal distributions are used. Algorithms for estimating the parameters of the model from the joint posterior distribution are derived and they are determined statistically from the posterior distribution using both Gibbs sampling a Markov chain Monte Carlo method and the iterated conditional modes algorithm a deterministic optimization technique for marginal mean and maximum a posterior estimates respectively.