TY - JOUR

T1 - Finding Bayesian Optimal Designs for Nonlinear Models

T2 - A Semidefinite Programming-Based Approach

AU - Duarte, Belmiro P.M.

AU - Wong, Weng Kee

N1 - Publisher Copyright:
© 2014 The Authors.

PY - 2015/8/1

Y1 - 2015/8/1

N2 - This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.

AB - This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.

UR - http://www.scopus.com/inward/record.url?scp=84938200226&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84938200226&partnerID=8YFLogxK

U2 - 10.1111/insr.12073

DO - 10.1111/insr.12073

M3 - Article

AN - SCOPUS:84938200226

SN - 0306-7734

VL - 83

SP - 239

EP - 262

JO - International Statistical Review

JF - International Statistical Review

IS - 2

ER -