This paper addresses the problem of creating probabilistic brain atlases from manually labeled training data. We propose a general mesh-based atlas representation, and compare different atlas models by evaluating their posterior probabilities and the posterior probabilities of their parameters. Using such a Baysian framework, we show that the widely used "average" brain atlases constitute relatively poor priors, partly because they tend to overfit the training data, and partly because they do not allow to align corresponding anatomical features across datasets. We also demonstrate that much more powerful representations can be built using content-adaptive meshes that incorporate non-rigid deformation field models. We believe extracting optimal prior probability distributions from training data is crucial in light of the central role priors play in many automated brain MRI analysis techniques.