# Inge S. Helland: Symmetry and model reduction

Inge S. Helland (Professor emeritus at Department of Mathematics,UiO) will give a seminar in the lunch area, 8th floor Niels Henrik Abels hus at 14:15.

**Title: **Symmetry and model reduction

**Abstract: **Statistics is the basis for most empirical sciences, and an interesting question is whether one can find links to other, complementary scientific cultures by taking statistical theory as a point of departure. I will show that the answer is yes for at least two cases if one adds the following structure to the statistical model paradigm: By suitable symmetry assumptions there may be a group of transformations defined on the sample space and a corresponding group of transformations defined on the parameter space. If the parameter group is not transitive, it induces several orbits on the parameter space. I will postulate that any model reduction should be to an orbit or to a set of orbits of the chosen group. First I illustrate this rule by giving several statistical examples. Then I show how the rule leads to the partial least squares model, and I indicate how one can derive the quantum theory for electron spin in this way. Some recent results on quantum probability are mentioned.