Sparse Bayesian inference methods are applied to decode three-dimensional (3D) reach to grasp movement based on recordings of primary motor cortical (M1) ensembles from rhesus macaque. For three linear or nonlinear models tested, variational Bayes (VB) inference in combination with automatic relevance determination (ARD) is used for variable selection to avoid overfitting. The sparse Bayesian linear regression model achieved the overall best performance across objects and target locations. We assessed the sensitivity of M1 units in decoding and evaluated the proximal and distal representations of joint angles in population decoding. Our results suggest that the M1 ensembles recorded from the precentral gyrus area carry more proximal than distal information.