Toward the Applicability of Statistics: A Representational View

Abstract

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.