Universal Principles, Approximation and Model Choices

Universal principles are ones which make no reference to the subject matter of the data and include Maximum Likelihood, Bayes, AIC and MDL. In this talk we criticize the use of such principles to solve the problem of model choice. The criticism will be mainly directed against MDL but corresponding arguments can be made against the other principles. A concept of approximation will be introduced and its use in choosing a model illustrated by examples from non-parametric statistics.