This paper presents a Bayesian framework for neonatal brain-tissue segmentation in clinical magnetic resonance (MR) images. This is a challenging task because of the low contrast-to-noise ratio and large variance in both tissue intensities and brain structures, as well as imaging artifacts and partial-volume effects in clinical neonatal scanning. We propose to incorporate a spatially adaptive likelihood model using a data-driven nonparametric statistical technique. The method initially learns an intensity-based prior, relying on the empirical Markov statistics from training data, using fuzzy nonlinear support vector machines (SVM). In an iterative scheme, the models adapt to spatial variations of image intensities via nonparametric density estimation. The method is effective even in the absence of anatomical atlas priors. The implementation, however, can naturally incorporate probabilistic atlas priors and Markov-smoothness priors to impose additional regularity on segmentation. The maximum-a-posteriori (MAP) segmentation is obtained within a graph-cut framework. Cross validation on clinical neonatal brain-MR images demonstrates the efficacy of the proposed method, both qualitatively and quantitatively.