Design of experiments for models involving profile factors

Abstract

In the traditional design of experiments, it is assumed that each run of the experiment involves the application of a treatment, consisting of static settings of the controllable factors. The objective of this work is to extend the usual optimal experimental design paradigm to modern experiments where the settings of factors are functions. Such factors are known as profile factors, or as dynamic factors. For these new experiments, the design problem is to identify optimal experimental conditions to vary the profile factors in each run of the experiment.

In general, functions are infinite dimensional objects. The latter produces challenges in estimation and design. To face the challenges, a new methodology using basis functions is developed. Primary focus is given on the B-spline basis system, due to its computational efficiency and useful properties. The methodology is applied to a functional linear model, and expanded to a functional generalised linear model, reducing the problem to an optimisation of basis coefficients. Special cases, including combinations of profile and scalar factors, interactions, and polynomial effects, are taken into consideration.

The methodology is demonstrated through multiple examples, aiming to find A- and D- optimal experimental designs. The sensitivity of optimal experimental conditions to changes in the settings of the profile factors and the functional parameters is extensively investigated. Bayesian optimal designs are identified through the addition of roughness penalties to penalise the complicated functions. The latter contributes in identifying the connection between the frequentist and the Bayesian approaches.

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Identifiers

ORCID for David Woods: orcid.org/0000-0001-7648-429X

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