Statistical Design of Experiments for Complex Nonparametric and Mechanistic Models

Experiments are used to investigate the impact on an observed response of a set of controllable features (called factors or variables) of the system under study, and provide the basis of much important research in many areas of the physical sciences, engineering and industry. Design of experiments is concerned with selecting the combinations of factor values, or treatments, to be run to meet the aims of the experiment with best use of resource. These aims will usually involve learning about the unknown relationship between the response and the factors, and then building a statistical model to approximate this relationship. Such a model describes how changing the factor values affects the response and the nature of the uncertainty in the relationship arising from sources such as measurement error. Importantly, the model allows us to predict the response from the system for an unobserved treatment, and to quantify our uncertainty about the prediction.

This research programme aims to develop new methods of finding good designs under a variety of different assumptions about the type of statistical model to be estimated from the experiment data in the presence of complicated structures in the data collection process. There are three research themes and, for each, new designs will be found that allow us to learn efficiently and effectively about different types of statistical models. In the first theme, we have little prior scientific knowledge about the system, and hence we cannot specify a form of statistical model in advance of the experiment. In the second theme, designs will be found for experiments where, for each treatment, we observe a curve or surface, representing a function, rather than a single number. We then need to learn about the form of this function for each treatment, and how the functions vary from treatment to treatment. The third theme will consider systems where one or more scientific theories may provide a mathematical approximation to the responses of interest. Here, a design is needed to generate data that enables discrimination between the competing theories and understanding of the difference, or discrepancy, between scientific theory and the real system.

Methodological research in the design of experiments has been traditionally motivated by problems from science, medicine and engineering. The research on the three themes is motivated by experimental programmes from pharmaceutical development, engineering and dispersion science. The new designs found will be test-bedded in prototype experiments in these fields through interactions with project partners and scientific collaborators. These experiments will provide a valuable evaluation of the methods and demonstrate their effectiveness to user communities. The methods will also have wider impact across a range of sciences and industry where such experiments are required and where there are currently no designs available tailored to both the aims of the experiment and the methods to be used in the data analysis.

The statistical design of experiments is crucial to the discovery of new knowledge in many fields of science and engineering. Those working in fields involving advanced technology and experiment techniques will potentially benefit from the optimal designs and methods developed in the research programme. They will be able to obtain data tailored to sophisticated modelling techniques, including understanding of uncertainties, and appropriate to their scientific aims. Importantly, the designs will make best use of resources, leading to efficient experiments.

Many industries are concerned with using experimental programmes to develop and manufacture products and processes with consistently high performance They are potential beneficiaries of the research through the availability of the new efficient tailored designs. This benefit leads to reduced cost of materials and faster time-to-market, offering the long-term prospect of improving UK economic competitiveness. Project partner GlaxoSmithKline and other pharmaceutical companies may make such gains in the development and manufacturing of new drugs. Collaborations with the Optoelectronics Research Centre and the National Centre for Advanced Tribology will lead to potential impact in other industries including communications, where technologies in fibre optics are leading the broadband revolution, and energy and transport through the generation of new lubricant technologies.

The research has potential societal impact by underpinning scientific advances that improve the quality of life and healthcare in the UK through the faster development of medicines. Societal impact would also come from application by Dstl of the new techniques to develop improved methods for sequential virtual and physical experiments to understand chemical and biological dispersion, thereby decreasing the time taken to react to a terrorist attack.

Interaction with project partners and collaborators provide the opportunity to transfer new statistical methods and techniques to other scientists, leading to an increase in the knowledge and skill-base amongst scientists and statisticians working in the collaborating organisations and centres.

In all the above fields, experiments are typically complex and involve the measurement of responses which require advanced statistical modelling techniques. There are currently no generic optimal or highly efficient designs available that are tailored to these types of experiments. The proposed research will provide the first bespoke designs and methods for these fast moving application areas, and others with similar types of experimentation, and hence enable greater scientific understanding than currently possible.