The semi-algebraic geometry of optimal designs for the Bradley-Terry model

01/08/2019

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by   Thomas Kahle, et al.

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Optimal design theory for nonlinear regression studies local optimality on a given design space. We identify designs for the Bradley--Terry paired comparison model with small undirected graphs and prove that every saturated optimal design is represented by a path. We discuss the case of 4 alternatives in detail and derive explicit polynomial inequality descriptions for optimality regions in parameter space.