The subject of this chapter is Bayesian decision theory and more specifically its use in data fusion. To keep the discussion focused we shall concentrate on the problem of classifying an unknown object into one of K possible classes. We start by considering the curve of dimensionality and how this impinges on the number of features to be used and their selection. We then consider the Naive Bayes classifier and its variants. These include the following Bayesian classifiers: tree augmented, homologous, boosted, committee and model average. We then generalize these classifiers to multiple classes. Finally we briefly consider non-Bayesian classifiers. The chapter includes several detailed examples.