Statistical models, intrinsic dependence and intrinsic inference (Q1094014)

To provide support for the point of view of intrinsic inference, types of dependence among the variables of models for statistical inference are discussed. They are related to (i) incomplete determination of specification and predictor variables and (ii) the existence of common factors among the variables. The argument is that, in a general experimental situation, it is not possible to know and control all the specification and predictor variables that might affect the response variables; a number of more or less relevant factor variables are left uncontrolled and unobserved. Because the unobserved factors may be present in some observations with certain modalities and in other observations with other modalities, the responses contain a degree of covariation across observations. This covariation implies modelling the observations as dependent random variables. Known approaches to modelling dependence are discussed and research in specific areas of application (analysis of variance, regression, finite sampling theory, Box-Jenkins models, Kriging) are summarized and related to the preceding discussion. A justification of the concept of generating system in terms of the dependence implied by the common factors and a comparison of Bayesian and intrinsic inference are also given.