On the feasibility of semi-algebraic sets in Poisson regression

TL;DR

This paper explores the use of computer algebra tools to analyze semi-algebraic regions of optimality in Poisson regression experimental design, addressing the challenge of unknown parameters.

Contribution

It introduces a method to study optimal design regions in Poisson regression using semi-algebraic sets and computational tools, advancing design theory.

Findings

Semi-algebraic regions of optimality can be characterized computationally.

Computer algebra tools effectively analyze complex design regions.

The approach aids in understanding local optimality in generalized linear models.

Abstract

Designing experiments for generalized linear models is difficult because optimal designs depend on unknown parameters. The local optimality approach is to study the regions in parameter space where a given design is optimal. In many situations these regions are semi-algebraic. We investigate regions of optimality using computer tools such as yalmip, qepcad, and Mathematica.