Conditioning in dynamic models

A statistical model is generally defined through a probability on some variables conditionally on other variables and refers to some parameters of interest. Therefore, it seems natural to ask under which conditions such a model does not lose information with respect to a model describing more variables and implying more parameters. Admissibility conditions for reductions by conditioning are investigated both in one-shot and in dynamic models. By so doing, concepts of ‘exogeneity’ and of ‘non-causality’ are integrated into a general framework. This paper is essentially a non-technical introduction to the theory of reduction developed more formally in other papers. It also supplies various examples of the concepts introduced in that theory