## AbstractThis chapter proposes a generative model and a Bayesian learning scheme for a classifier that takes uncertainty at all levels of inference into account. Classifier inputs will be uncertain if they are estimated, for example using a preprocessing method. Classical approaches would neglect the uncertainties associated with these variables. However, the decisions thus found are not consistent with Bayesian theory. In order to conform with the axioms underlying the Bayesian framework, we must incorporate all uncertainties into the decisions. The model we use for classification treats input variables resulting from preprocessing as latent variables. The proposed algorithms for learning and prediction fuse information from different sensors spatially and across time according to its certainty. In order to get a computationally tractable method, both feature and model uncertainty of the preprocessing stage are obtained in closed form. Classification requires integration over this latent feature space, which in this chapter is done approximately by a Markov chain Monte Carlo (MCMC) method. Our approach is applied to classifying cognitive states from EEG segments and to classification of sleep spindles
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