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Title: Sequential multi-objective planning of factorial experiments with restricted randomisation Authors:  Steven Gilmour - KCL (United Kingdom)
Kalliopi Mylona - King's College London (United Kingdom)
Olga Egorova - King's College London (United Kingdom) [presenting]
Abstract: Implementing a series of controlled experiments in order to study a relationship between a response and a set of parameters of the process of interest is a common approach in various applications. It might be organised as a sequence of a pre-determined number of batches, or with potential additional experiments on the agenda, and it is sensible to devise a strategy of approaching the optimal design search for such frameworks sequentially as well. We focus on sequential planning of factorial experiments, including the cases of restricted randomisation. The design search methodology is constructed with multiple objectives, corresponding to (1) the quality of inference and prediction, and (2) ensuring robustness of the fitted model against potential model misspecification and managing the lack-of-fit. Gathered data and interim inference are utilised for planning the next stage through shaping the primary model and amending optimality criteria functions, including Bayesian updating of the parameters. We consider an example of a split-plot experimental setting and construct a set of Pareto-optimal designs; some particularities of the sequential planning and the choices that are to be made by the experimenters are discussed.