This paper introduces a multivariate Bayesian (MVB) scheme to decode or recognise brain states from neuroimages. It resolves the ill-posed many-to-one mapping, from voxel values or data features to a target variable, using a parametric empirical or hierarchical Bayesian model. This model is inverted using standard variational techniques, in this case expectation maximisation, to furnish the model evidence and the conditional density of the model's parameters. This allows one to compare different models or hypotheses about the mapping from functional or structural anatomy to perceptual and behavioural consequences (or their deficits). We frame this approach in terms of decoding measured brain states to predict or classify outcomes using the rhetoric established in pattern classification of neuroimaging data. However, the aim of MVB is not to predict (because the outcomes are known) but to enable inference on different models of structure-function mappings; such as distributed and sparse representations. This allows one to optimise the model itself and produce predictions that outperform standard pattern classification approaches, like support vector machines. Technically, the model inversion and inference uses the same empirical Bayesian procedures developed for ill-posed inverse problems (e.g., source reconstruction in EEG). However, the MVB scheme used here extends this approach to include a greedy search for sparse solutions. It reduces the problem to the same form used in Gaussian process modelling, which affords a generic and efficient scheme for model optimisation and evaluating model evidence. We illustrate MVB using simulated and real data, with a special focus on model comparison; where models can differ in the form of the mapping (i.e., neuronal representation) within one region, or in the (combination of) regions per se.