A statistical interpretation of existing parallel magnetic resonance imaging methods reveals that the underlying noise model is of additive independent Gaussian noise. In reality MR imaging processes suffer from a variety of noise, errors and other uncertainties. A careful statistical analysis of these uncertainties can potentially allow significant improvement of the reconstruction process. In this paper we present such an analysis and describe a few very recent approaches to handle these statistical models. We show examples of simulation and in vivo reconstructed data which demonstrate the potential of the statistical approach.