This paper introduces a new supervised Bayesian approach to hyperspectral image segmentation, with two main steps: (a) learning, for each class label, the posterior probability distributions, based on a multinomial logistic regression model; (b) segmenting the hyperspectral image, based on the posterior probability distribution learnt in step (a) and on a multi-level logistic prior encoding the spatial information. The multinomial logistic regressors are learnt by using the recently introduced LORSAL (logistic regression via splitting and augmented Lagrangian) algorithm. The maximum a posterior segmentation is efficiently computed by the α-Expansion min-cut based integer optimization algorithm. Aiming at reducing the costs of acquiring large training sets, active learning is performed using a mutual information based criterion. State-of-the-art performance of the proposed approach is illustrated with simulated and real hyperspectral data sets in a number of experimental comparisons with recently introduced hyperspectral classification methods.