Abstract for the talk on 07.04.2020 (17:40 h)Nonlinear Algebra Seminar Online (NASO)
Frank Röttger (MPI MIS, Leipzig)
Geometry of Optimal Design for Generalized Linear Models
See the video of this talk.
Design of experiments (DoE) for generalized linear models (GLM) is a recurring topic for practitioners and statisticians. We introduce basic notions and tools from GLM and DoE and see that there exists a fruitful connection between DoE and algebraic structures, namely varieties and semi-algebraic sets. This happens because the optimality conditions of experimental designs are often given as algebraic constraints on the parameters of the GLM. We exemplify this approach for the Bradley-Terry paired comparison model, where we compute the exact solutions for the optimal designs for a small example.