Algebraic geometry of Poisson regression

Thomas Kahle, Kai-Friederike Oelbermann, Rainer Schwabe


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.


algebraic statistics; optimal experimental design; Poisson regression; semi-algebraic sets; spectrahedra

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