Algebraic geometry of Poisson regression

Algebraic geometry of Poisson regression AS2015 Special Issue articles: This issue includes a series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics Conference held in Genoa, Italy, in June 2015. Special issue guest editors: Piotr Zwiernik and Fabio Rapallo. Kahle, Thomas Creator Faculty thomas.kahle@ovgu.de Oelbermann, Kai-Friederike Creator Schwabe, Rainer Creator MATH / Applied Mathematics Illinois Institute of Technology Affiliated department algebraic statistics optimal experimental design Poisson regression semi-algebraic sets spectrahedra 2016 2016-07-12 Designing experiments for generalized linear models is difficult because optimal designs depend on unknown parameters. Here we investigate local optimality. We propose to study for a given design its region of optimality in parameter space. Often these regions are semi-algebraic and feature interesting symmetries. We demonstrate this with the Rasch Poisson counts model. For any given interaction order between the explanatory variables we give a characterization of the regions of optimality of a special saturated design. This extends known results from the case of no interaction. We also give an algebraic and geometric perspective on optimality of experimental designs for the Rasch Poisson counts model using polyhedral and spectrahedral geometry. Article