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Title: Designing experiments for general network structures Authors:  Ming-Chung Chang - Graduate Institute of Statistics, National Central University (Taiwan) [presenting]
Frederick Kin Hing Phoa - Academia Sinica (Taiwan)
Jing-Wen Huang - National Tsing-Hua University, institute of statistics (Taiwan)
Abstract: Experiments on connected units are commonly conducted in various fields, such as agriculture trials, medical experiments and social networks. In these cases, an experimental unit may connect with some others, and the treatment applied to a unit has an effect, called a network effect, on the responses of the neighboring units. Designing such experiments is rarely discussed in the literature. A study of A-optimal designs on connected experimental units with unstructured treatments has been previously initiated. It was assumed that the network effects are unknown constants. We study a similar design problem but assuming that those effects are random effects, which lead to a property that the responses of two units are correlated if some neighbors of one unit and those of the other receive the same treatment. Alphabetical optimality criteria are considered for selecting good designs with high efficiency of estimating the treatment effects and/or high accuracy of predicting the network effects. We provide theoretical conditions for designs to be optimal and illustrate our theory with some numerical examples.