Woods, EPSRC, 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.