We present some details of Bayesian block sparse modeling using hierarchical prior having deterministic and random parameters when entries within the blocks are correlated. In particular, the effect of the threshold to prune out variance parameters of algorithms corresponding to several choices of marginals, viz. multivariate Jeffery prior, multivariate Laplace distribution and multivariate Student’s t distribution, is discussed. We also provide details of experiments with Electroencephalograph (EEG) data which shed some light on the possible applicability of the proposed Sparse Variational Bayes framework. © Springer Nature Switzerland AG 2019.