  In this article, the notion of a mathematical model in science is attempted
to be enlightened from several points of view. In particular, it is shown that
mathematical models are introduced differently and used differently in
different areas of science. In the present article the use of models in
statistics is taken as a basis, but links are given to several other areas. Two
particular such links are described in some detail here: First the link
connected to the chemometrical Partial Least Squares algorithm, a link that now
has been generalized to the more sophisticated envelope model. Secondly,
statistics, as is well known, relies heavily on making decisions, and it may
also in certain cases be connected to a process of taking measurements. A
mathematical model for these two activities, connected to the mind of an
observer, is introduced. This model is taken further, and shown to be important
in a new proposal for a foundation of quantum theory. Quantum mechanics, as
seen from this point of view, is described in some detail. The discussion here
is close to the discussion in a recent book and in recently published articles
by the author.
