Advances in algorithms for electromagnetic brain imaging have relevance in extending non-invasive BCI with EEG or MEG by using brain source space level reconstructions. Our recent work in brain source reconstruction includes Bayesian inference algorithms for joint estimation of signal and structured noise in sparse linear models. We leverage the majorization-minimization framework for both unifying different Bayesian algorithms, and extending this joint signal and noise inference for novel adaptive beamforming. We demonstrate that this approach has higher fidelity when compared to benchmarks. We then combine source reconstructed data with biophysically based spectral graph modeling of neural oscillations that includes structural connectome data from diffusion MRI. Bayesian inference of biophysical parameters from SGM models can serve as parsimonious and sensitive biomarkers for Alzheimer’s disease monitoring as well as for BCI applications.