Advanced Topics in Optimal Design
In many experimental situations, the assumptions of a homogeneous variance and uncorrelated observations are no longer satisfied. However, the design of experiments under these circumstances has only recently received attention. In this chapter, we give a concise overview of the work that has been done when the experimental observations do not have a constant variance and when the observations are correlated to each other. We also examine the design of experiments when the experimental units are heterogeneous. In that case, the experiment has to be blocked. Throughout this chapter, we show how the information matrix for each of the experiments can be written as a sum of outer products of vectors. This is extremely important for design construction algorithms because it allows a fast update of the information matrix, its determinant and its inverse.
KeywordsOptimal Design Block Size Central Composite Design Design Point Block Effect
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