This chapter reviews the fundamentals of inference, and gives a motivation for Bayesian analysis. The method is illustrated with dependency tests in data sets with categorical data variables, and the Dirichlet prior distributions. Principles and problems for deriving causality conclusions are reviewed, and illustrated with Simpson’s paradox. The selection of decomposable and directed graphical models illustrates the Bayesian approach. Bayesian and EM classification is shortly described. The material is illustrated on two cases, one in personalization of media distribution, one in schizophrenia research. These cases are illustrations of how to approach problem types that exist in many other application areas.