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Multi-channel linear prediction (MCLP) can model the late reverberation in the short-time Fourier transform domain using a delayed linear predictor and the prediction residual is taken as the desired early reflection component. Traditionally, a Gaussian source model with time-dependent precision (inverse of variance) is considered for the desired signal. In this paper, we propose a Student's t-distribution model for the desired signal, which is realized as a Gaussian source with a Gamma distributed precision. Further, since the choice of a proper MCLP order is critical, we also incorporate a Gaussian distribution prior for the prediction coefficients and a higher order. We consider a batch estimation scenario and develop variational Bayes expectation maximization (VBEM) algorithm for joint posterior inference and hyper-parameter estimation. This has lead to more accurate and robust estimation of the late reverb component and hence its cancellation, benefitting the desired residual signal estimation. Along with these stochastic models, we formulate single channel output (MISO) and multi channel output (MIMO) schemes using shared priors for the desired signal precision and the estimated MCLP coefficients at each microphone. Experiments using real room impulse responses show improved late reverberation suppression with the proposed VBEM approach over the traditional methods, for different room conditions. Additionally, we achieve a sparse coefficient vector for the MCLP avoiding the criticality of manually choosing the model order. The MIMO formulation is easily extended to include spatial filtering of the enhanced signals, which further improves the estimation of the desired signal.