Classical, Bayesian and intrinsic inference (Q1081990)

Broadly speaking, intrinsic inference is based on populations of random units, unlike (ordinary) statistical inference in which statements about a population are made on the basis of a random sample. Thus intrinsic inference takes cognisance of the dependence among observations, and, it is claimed, ''accurately represents the deductive-inductive inferential procedure commonly adopted in empirical sciences.'' In this paper the intrinsic inference model is contrasted with the models for classical and Bayesian inference, and a Bayesian intrinsic inference model is proposed which has the advantage of keeping separate the different parts of the scientific model. One of the most important results emerging from this study is that, no matter what the intrinsic dependence may be, if the units are selected by simple random sampling, the sample probability function is exchangeable. This suggests that exchangeability is a more satisfactory basis for mathematical statistics than independence.