Bayesian classification derivation tree. A tree summarizing the relationships between several important quantities in the general theoretical framework of Bayesian classification. A directed edge between a parent and its child indicates that the child can be derived from the parent by the equations indicated in the edge label. The root of the tree p(θ|S
) is the posterior distribution of the feature label parameters and by taking expectations with respect to this distribution, we can derive the effective class conditional densities p(x|y,S
) and the distribution of the classifier error p(ε|S
). Then these quantities give rise to the OBC, and MMSE and MSE estimates for the error as described in the text. Quantities highlighted in grey are given in closed form for Gaussian and multinomial distributions in .