The Bayesian Source Separation model is diﬀerent from the Bayesian Regression model in that the sources are unobserved and from the Bayesian Factor Analysis model in that there may be more or less sources than the observed dimension (the number of microphones). Further, in the Bayesian Factor Analysis model, the variance of the unobserved factor score vectors is a priori assumed to be unity and diagonal for Psychologic reasons. The Bayesian Source Separation model [52, 57, 58, 59, 60, 62, 63] allows the covariance matrix for the unobserved sources to have arbitrary variances. That is, the covariance matrix for the sources is not required to be diagonal and also the sources are allowed to have a mean other than zero. With a general covariance matrix (one that is not constrained to be diago-
nal), the sources or speakers at the cocktail party are allowed to be dependent or correlated. There are other models which impose either the constraint of orthogonal sources  or the constraint of independent sources . If the sources are truly orthogonal or independent, then such models would be appropriate (independent sources can be obtained here by imposing constraints). However, if the sources are not independent as in the “real-world” cocktail party problem, then an independence constraint would not be appropriate.