A Model for Bayesian Source Separation with the Overall Mean

Typically in source separation models the overall mean as well as the mean of the sources are assumed to be zero. This paper assumes a nonzero overall mean and a nonzero source mean, quantifies available prior knowledge regarding them and other parameters. This prior knowledge is incorporated into the inferences along with the current data in the Bayesian approach to source separation. Vague, conjugate normal, and generalized conjugate normal distributions are used to quantify knowledge for the overall mean vector. Algorithms for estimating the parameters of the model from the joint posterior distribution are derived and 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. This is a methodological paper which outlines the model without the use of a numerical example.