Bayesian optimal designs for nonlinear models with three or four parameters
نویسندگان
1 Department of Mathematics, Faculty of Basic Sciences, Ayatollah Boroujerdi University, Boroujerd, Iran.
2 Department of Mechanical Engineering, Sahand University of Technology, Tabriz, Iran.
doi
10.22034/jirss.2025.2071511.1135چکیده
In design of experiments, optimal design is an important approach that maximizes the chances of experimental success. A- and D-optimality are well-known criteria for identifying optimal designs. In nonlinear models, these criteria depend on unknown parameters, complicating the design derivation. This paper uses the Bayesian method to address this, deriving A- and D-optimal designs for EMAX, log-linear, and LINEXP models with three or four parameters, using uniform priors. Optimal designs with minimum support points are obtained, with varying weights. These designs serve as benchmarks for evaluating practical alternative designs. Two alternatives were assessed, showing over 80\% efficiency in most models compared to A- and D-optimal designs. The computations in this study were performed using a numerical nonlinear approach, specifically the NLPSolve method, which is included in the Optimization package in Maple software.
