Talk
Geometry of Optimal Design for Generalized Linear Models
- Frank Röttger (MPI MiS, Leipzig)
Abstract
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.
