arXiv subjects

Ben M. Parker

Publications and source records attributed to Ben M. Parker.

3 recordsLinked to original sources

arXiv2021

Designs with complex blocking structures and network effects for agricultural field experiments

We propose a novel model-based approach for constructing optimal designs with complex blocking structures and network effects, for application in agricultural field experiments. The potential interference among treatments applied to different plots is described via a network structure, defined via the adjacency matrix. We consider a field trial run at Rothamsted Research and provide a comparison of optimal designs under various different models, including the commonly used designs in such situations. It is shown that when there is interference between treatments on neighbouring plots, due to the spatial arrangement of the plots, designs incorporating network effects are at least as, and often more efficient than, randomised row-column designs. The advantage of network designs is that we can construct the neighbour structure even for an irregular layout by means of a graph to address the particular characteristics of the experiment. The need for such designs arises when it is required to account for treatment-induced patterns of heterogeneity. Ignoring the network structure can lead to imprecise estimates of the treatment parameters and invalid conclusions.

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arXiv2019

Optimal block designs for experiments on networks

We propose a method for constructing optimal block designs for experiments on networks. The response model for a given network interference structure extends the linear network effects model to incorporate blocks. The optimality criteria are chosen to reflect the experimental objectives and an exchange algorithm is used to search across the design space for obtaining an efficient design when an exhaustive search is not possible. Our interest lies in estimating the direct comparisons among treatments, in the presence of nuisance network effects that stem from the underlying network interference structure governing the experimental units, or in the network effects themselves. Comparisons of optimal designs under different models, including the standard treatment models, are examined by comparing the variance and bias of treatment effect estimators. We also suggest a way of defining blocks, while taking into account the interrelations of groups of experimental units within a network, using spectral clustering techniques to achieve optimal modularity. We expect connected units within closed-form communities to behave similarly to an external stimulus. We provide evidence that our approach can lead to efficiency gains over conventional designs such as randomized designs that ignore the network structure and we illustrate its usefulness for experiments on networks.

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arXiv2018

A graph-theoretic framework for algorithmic design of experiments

In this paper, we demonstrate that considering experiments in a graph-theoretic manner allows us to exploit automorphisms of the graph to reduce the number of evaluations of candidate designs for those experiments, and thus find optimal designs faster. We show that the use of automorphisms for reducing the number of evaluations required of an optimality criterion function is effective on designs where experimental units have a network structure. Moreover, we show that we can take block designs with no apparent network structure, such as one-way blocked experiments, row-column experiments, and crossover designs, and add block nodes to induce a network structure. Considering automorphisms can thus reduce the amount of time it takes to find optimal designs for a wide class of experiments.

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