Construction of Optimal Designs for Nonlinear Models

Download or read book Construction of Optimal Designs for Nonlinear Models written by Anh Nam Tran and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Choosing a good design which can draw a sufficient inference about parameters is essential before conducting an experiment. Dependence between information matrix and model parameters of nonlinear models is an existed conundrum. Seeking optimal design for nonlinear models is our main goal in this thesis. So we start with a general overview of optimal design theory both for linear and nonlinear models. A variety of criteria and their properties are discussed. Some of the bedrock of the theory of optimal design, such as convex design, directional derivatives and general equivalence theorem are considered as well. We review a class of algorithms which are commonly used in practice to search for optimal design of linear models. We then extend these approaches and develop some strategies for constructing optimal designs for nonlinear models. Motivated by the fact that Bayesian methods are ideally suited to contribute to experimental design for nonlinear models, we construct Bayesian optimal designs by incorporating prior information and uncertainties regarding the statistical model. In our Bayesian framework, we consider a discretization of the parameter space to efficiently represent the posterior distribution. We construct optimal designs for some logistic models using a clustering approach and a group sequential multiplicative algorithm. The idea is that, at an appropriate iterate, the single distribution is replaced by conditional distributions within clusters and a marginal distribution across the clusters. Our group sequential method along with the clustering approach provides a novel and powerful method for constructing optimal designs based on nonlinear models. Finally, we develop another novel method in order to obtain prior information on the model parameters by using meta-analysis for constructing optimal designs for nonlinear models. As the prior information on the parameters is rarely known in practice, optimal designs obtained using this method will be more effective in drawing inference for the parameters.