Model statistical structures

This third block is dedicated to the implications of the consistency constraints on the statistical families of distributions used when building stochastic models. In particular we show that some families cannot be used unless the random variable is dimensionless. In particular the dimensionless ratios provided by the Bauckingham theorem arise as natural candidates for these distributions. We also deal with how to define multivariate models and present underdetermined, overdetermined and strictly determined methods, indicating about some warnings when using these alternatives. In particular, we suggest the use of Bayesian networks as the best way of defining multivariate models, because of the fact that they always satisfy consistency and have a clear physical interpretation.