Toward the Applicability of Statistics: A Representational View

The problem of understanding how statistical inference is, and can be, applied in empirical sciences is important for the methodology of science. It is the objective of this paper to gain a better understanding of the role of statistical methods in scientific modeling. The important question of whether the applicability reduces to the representational properties of statistical models is discussed. It will be shown that while the answer to this question is positive, representation in statistical models is not purely structural. In spite of the fact that representation in statistical models is based on the structural similarities between the statistical model and the empirical systems under study, these relationships are shown to be appropriate for representing relations in the target system by agent function, too. A second aspect of the paper involves the claim that agent-based components of statistical modeling are: a) interpretation of random variables, b) selection of the goal of statistical research, and c) selection of estimator properties. To justify these claims, a preliminary discussion will be presented on the role of statistics in modeling, as in regression and other structural models. This role will be explored and realized using a structural viewpoint. Also the role of statistical estimation in statistical modeling is discussed to explain the representational role of models and the inferential role of the agent in modeling.