Optimal Design of Experiments

Overview

Topic status: We're looking for students to study this topic.

In model-based design of experiments we are often interested in collecting data to fit and estimate statistical models. Experiments can be, but quite often are not, designed "optimally", where "optimal" typically means parameter estimates with high precision, i.e., minimum variance. Optimal designs require less number of observations to estimate parameters with the same, or higher, precision than non-optimal designs. Hence optimal designs can reduce the "costs" of experimentation. Practically this can mean: reduced economic costs; reduced loss of life/health; reduced loss of quality; etc. Various projects are available, of which only three are listed below.

  • Numerical Algorithms for Constructing Optimal Designs
    Although the theory of optimal design is well established, there is little in the design literature related to the development of algorithms for constructing such optimal designs. The aim of this project is to investigate numerical algorithms for constructing optimal designs. Hence this project combines areas of optimum experimental design (e.g., probability distributions, log-likelihood functions, information matrices) and optimisation theory (e.g., multiplicative algorithms, gradient methods, numerical analysis).
  • Approximation Methods in Non-linear Optimal Design
    The likelihood function for non-linear models, such as non-linear mixed models, can be intractable and involve difficult numerical integrations. Problems with intractable likelihoods can also occur in some classes of linear models, such as stochastic frontier models. This poses a challenge in designing experiments based on such models, since information matrices, which are derived from log-likelihood functions, are used to construct optimal designs. Approximation methods, typically based on Taylor series approximations, are frequently employed to deal with the difficult numerical integrations. This project aims to investigate and assess the performance of approximation methods used in the non-linear optimal design of experiments.
  • Clinical Trial Design
    Before a pharmaceutical drug or device is approved for use in the general public, rigourous experimentation is conducted to ensure the efficacy (how well it works) and safety (are there any side effects) of the product. Such experiments are called clinical trials. Optimal design is an objective model-based approach to the design of clinical trials. Various projects are available on optimal design of clinical trials.
Study level
Honours
Supervisors
QUT
Organisational unit

Science and Engineering Faculty

Research area

Mathematical Sciences

Contact

Please contact the supervisor.