Bayesian optimal designs for efficient estimation of the optimum point with generalised linear models

Most of the current development of optimal designs focus on a globally well-estimated model or the model parameter vector as a whole. For many applications, however, the design objective is to estimate the optimum point that optimises the system performance. In such cases, an efficient design should collect data informative about the optimum point instead of the whole regression model. In this article, we develop a Bayesian optimal design framework for efficient estimation of the optimum point with generalised linear models (GLMs). The developed framework proposes a Bayesian optimality criterion based on the expected Shannon information gain on the optimum point. An algorithm to evaluate the analytically intractable design criterion is also proposed. We motivate, develop and illustrate this framework with an example from semiconductor manufacturing, where the experiment objective is to optimise the etching step to minimise the surface defects on the wafers.