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Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.

Belmiro P M Duarte1, Weng Kee Wong2

  • 1Department of Chemical and Biological Engineering, ISEC, Polytechnic Institute of Coimbra, R. Pedro Nunes, 3030-199 Coimbra, Portugal ; GEPSI, CIEPQPF, Department of Chemical Engineering, University of Coimbra, R. Sílvio Lima, Pólo II, 3030-790 Coimbra, Portugal.

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|October 30, 2015
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Summary
This summary is machine-generated.

This study introduces Bayesian optimal design for nonlinear regression using semidefinite programming (SDP). It extends optimal design formulation to nonlinear models, employing Gaussian quadrature formulas (GQF) for criteria like D-optimality.

Keywords:
Approximate designsGaussian quadrature formulasnonlinear modelssemidefinite programming

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Area of Science:

  • Statistics
  • Mathematical Modeling

Background:

  • Optimal design is crucial for efficient statistical inference.
  • Extending optimal design to nonlinear models presents computational challenges.

Purpose of the Study:

  • To develop a Bayesian optimal design method for nonlinear regression models.
  • To extend the formulation of optimal design problems as semidefinite programming (SDP) from linear to nonlinear models.

Main Methods:

  • Utilizing semidefinite programming (SDP) for constructing Bayesian optimal designs.
  • Employing Gaussian quadrature formulas (GQF) to compute expectations in Bayesian design criteria (e.g., D-, A-, E-optimality).

Main Results:

  • Demonstrated the approach using the power-logistic model, comparing with existing literature.
  • Investigated the impact of design space discretization, parameter uncertainty, GQF choices, and prior distributions on optimal design.

Conclusions:

  • The SDP approach provides a robust framework for Bayesian optimal design in nonlinear regression.
  • The method is applicable to various nonlinear models, including logistic and generalized linear models.