Algebraic geometry of Poisson regression

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 interest...

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Bibliographic Details
Published in:arXiv.org 2015-10
Main Authors: Kahle, Thomas, Kai-Friederike Oelbermann, Schwabe, Rainer
Format: Article
Language:English
Subjects:
Algebra
Design
Generalized linear models
Optimization
Parameters
Poisson density functions
Statistical analysis
Statistical models
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1510.05261